Dylan  Iqbal

Dylan Iqbal

1650271404

College Algebra - Version [π] Corrected Edition (PDF Textbook for FREE Download)

An introductory text for a college algebra survey course. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes.

  • Publication date: 04 Jul 2013
  • ISBN-10: n/a
  • ISBN-13: n/a
  • Paperback: 716 pages
  • Type: Textbook
  • Publisher: Self-publishing
  • License: Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported

"Functions First" Approach:

Stitz and Zeager wrote:

...A casual glance through the Table of Contents of most of the major publishers’ College Algebra books reveals nearly isomorphic content in both order and depth. Our Table of Contents shows a different approach, one that might be labeled "Functions First." To truly use The Rule of Four, that is, in order to discuss each new concept algebraically, graphically, numerically and verbally, it seems completely obvious to us that one would need to introduce functions first. (Take a moment and compare our ordering to the classic "equations first, then the Cartesian Plane and THEN functions" approach seen in most of the major players.) We then introduce a class of functions and discuss the equations, inequalities (with a heavy emphasis on sign diagrams) and applications which involve functions in that class.
Exercises:

Stitz and Zeager wrote:

The material is presented at a level that definitely prepares a student for Calculus while giving them relevant Mathematics which can be used in other classes as well. Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. The answers to nearly all of the computational homework exercises are given in the text and we have gone to great lengths to write some very thought provoking discussion questions whose answers are not given. One will notice that our exercise sets are much shorter than the traditional sets of nearly 100 "drill and kill" questions which build skill devoid of understanding. Our experience has been that students can do about 15-20 homework exercises a night so we very carefully chose smaller sets of questions which cover all of the necessary skills and get the students thinking more deeply about the Mathematics involved.

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College Algebra - Version [π] Corrected Edition (PDF Textbook for FREE Download)
Dylan  Iqbal

Dylan Iqbal

1649992891

Linear Algebra And Analysis (PDF Textbook for FREE Download)

This is on linear algebra and its interaction with analysis. It emphasizes the main ideas, both algebraic and geometric and attempts to present these ideas as quickly as possible without being overly terse.

  • Publication date: 13 Jan 2018
  • Paperback: 619 pages
  • Type: Textbook
  • Publisher: Self-publishing

From the Preface:

Kuttler wrote:

This is on linear algebra and its interaction with analysis. It emphasizes the main ideas, both algebraic and geometric and attempts to present these ideas as quickly as possible without being overly terse. The emphasis will be on arbitrary fields in the first part and then later geometric ideas will be included in the context of the usual fields of R and C. The first part is on linear algebra as a part of modern algebra. It avoids cluttering the presentation with geometric and analytic ideas which are really not essential to understanding these theorems. The second part is on the role of analysis in linear algebra. It is like baby functional analysis. Some analysis ideas do in fact creep in to the first part, but they are generally fairly rudimentary, occur as examples, and will have been seen in calculus. It may be that increased understanding is obtained by this kind of presentation in which that which is purely algebraic is presented first. This also involves emphasizing the minimum polynomial more than the characteristic polynomial and postponing the determinant. In each part, I have included a few related topics which are similar to ideas found in linear algebra or which have linear algebra as a fundamental part.The third part of the book involves significant ideas from analysis which depend on linear algebra. 

The book is a re written version of an earlier book. It also includes several topics not in this other book including a chapter which is an introduction to modules and rings and much more material on analysis. However, I am not including topics from functional analysis so much. Instead, I am limiting the topics to the standard analysis involving derivatives and integrals. In fact, if everything which uses linear algebra were presented, the book would be much longer. It is limited to topics that I especially like and emphasizes finite dimensional situations.  

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Linear Algebra And Analysis (PDF Textbook for FREE Download)
Dylan  Iqbal

Dylan Iqbal

1649920367

Linear Algebra I (PDF Textbook for FREE Download)

This book is an attempt to make the subject of linear algebra as understandable as possible, for a first time student of the subject.

  • Publication date: 01 Feb 2016
  • Paperback: 213 pages
  • Type: Textbook
  • License: Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported

From the Introduction:
Gregg Waterman wrote:

This book is an attempt to make the subject of linear algebra as understandable as possible, for a first time student of the subject. I developed the book from a set of notes used to supplement a standard textbook used when I taught the course in the past. At the end of the term I surveyed the students in the class, and the vast majority of them thought that the supplemental notes that I had provided would have been an adequate resource for them to learn the subject. Encouraged by this, I put further work in to correcting errors, adding examples and including material that I had left to the textbook previously. Here is the result, in its fourth edition. 

You should look at the table of contents and page through the book a bit at first to see how it is organized. Note in particular that each section begins with statements of the performance criteria addressed in that section. Performance criteria are the specific things that you will be expected to do in order to demonstrate your skills and your understanding of concepts. Within each section you will find examples relating to those performance criteria, and at the end of each chapter are exercises for you to practice your skills and test your understanding.

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Linear Algebra I (PDF Textbook for FREE Download)
Dylan  Iqbal

Dylan Iqbal

1649919920

College Algebra (PDF Textbook for FREE Download)

This course is an in-depth introduction to functions. Our study will be guided by some goals, and related essential questions that are designed to get at the essence of the idea of a function. 

  • Publication date: 01 May 2015
  • Paperback: 309 pages
  • Type: Textbook
  • License: Creative Commons Attribution 4.0 International

From the Introduction:
Gregg Waterman wrote:

This textbook is designed to provide you with a basic reference for the topics within. That said, it cannot learn for you, nor can your instructor; ultimately, the responsibility for learning the material lies with you. Before beginning the mathematics, I would like to tell you a little about what research tells us are the best strategies for learning. Here are some of the principles you should adhere to for the greatest success:

This course is an in-depth introduction to functions. Our study will be guided by some goals, and related essential questions that are designed to get at the essence of the idea of a function. 
Course Goals 
The overall goal of this course is to understand the concept of a function. This is a multi-faceted task, to be accomplished by developing several more specific understandings related to functions:

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College Algebra (PDF Textbook for FREE Download)
Dylan  Iqbal

Dylan Iqbal

1649909892

Algebra: A Computational Introduction (PDF Textbook for FREE Download)

This text is an introduction to algebra for undergraduates who are interested in careers which require a strong background in mathematics.

  • Publication date: 31 Dec 2009
  • Paperback: 419 pages
  • Type: Textbook
  • License: Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Generic

From the Preface:
John Scherk wrote:

This text is an introduction to algebra for undergraduates who are interested in careers which require a strong background in mathematics. It will benefit students studying computer science and physical sciences, who plan to teach mathematics in schools, or to work in industry or finance. The book assumes that the reader has a solid background in linear algebra. For the first 12 chapters elementary operations, elementary matrices, linear independence and rank are important. In the second half of the book abstract vector spaces are used. Students will need to have experience proving results. Some acquaintance with Euclidean geometry is also desirable. In fact I have found that a course in Euclidean geometry fits together very well with the algebra in the first 12 chapters. But one can avoid the geometry in the book by simply omitting chapter 7 and the geometric parts of chapters 9 and 18. 

The material in the book is organized linearly. There are few excursions away from the main path. The only significant parts which can be omitted are those just mentioned, the section in chapter 12 on P SL(2, Fp), chapter 13 on abelian groups and the section in chapter 14 on Berlekamp's algorithm.

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Algebra: A Computational Introduction (PDF Textbook for FREE Download)
Dylan  Iqbal

Dylan Iqbal

1649908828

Introduction to Modern Algebra (PDF Textbook for FREE Download)

A textbook for Math 225 Modern Algebra Course in Department of Mathematics and Computer Science at Clark University.

  • Publication date: 05 Dec 2017
  • Paperback: 179 pages
  • Type: Textbook

From the Course Webpage:
David Joyce wrote:

Course goals.

  • To provide students with a good understanding of the theory of modern algebra as described in the syllabus.
  • To help students develop the ability to prove theorems and solve problems.
  • To introduce students to some of the basic methods of modern algebra.
  • To develop abstract and critical reasoning by studying logical proofs and the axiomatic method as applied to modern algebra.
  • To make connections between modern algebra and other branches of mathematics, and to see some of the history of the subject.


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Introduction to Modern Algebra (PDF Textbook for FREE Download)
Dylan  Iqbal

Dylan Iqbal

1649906263

Elementary Algebra (PDF Textbook for FREE Download)

This book provides very clear and comprehensive coverage of the usual Elementary Algebra topics, as well as some Intermediate Algebra material. It provides plenty of examples and very robust, well-constructed exercise sets.

Publisher: The Saylor Foundation
Publication date: 01 Jan 2011
License: Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported
Document Type: Textbook

Excerpts from the Preface:

It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, elementary algebra and intermediate algebra. This textbook, Elementary Algebra, is the first part, written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course.This text is, by far, the best elementary algebra textbook offered under a Creative Commons license. It is written in such a way as to maintain maximum flexibility and usability. A modular format was carefully integrated into the design. For example, certain topics, like functions, can be covered or omitted without compromising the overall flow of the text. An introduction of square roots in Chapter 1 is another example that allows for instructors wishing to include the quadratic formula early to do so. Topics such as these are carefully included to enhance the flexibility throughout. This textbook will effectively enable traditional or nontraditional approaches to elementary algebra. This, in addition to robust and diverse exercise sets, provides the base for an excellent individualized textbook instructors can use free of needless edition changes and excessive costs! A few other differences are highlighted below: 

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#algebra #math #ebook #textbook #book 

Elementary Algebra (PDF Textbook for FREE Download)

Algebra 2 Introduction, Basic Review, Factoring, Slope, Absolute Value, Linear, Quadratic Equations

This algebra 2 introduction / basic review lesson video tutorial covers topics such as solving linear equations, absolute value equations, inequalities, and quadratic equations.  It shows you how to factor trinomials and polynomials in addition to simplify rational and radical expressions.  This video contains a ton of examples and practice problems.
Here is a list of topics:
1.  Algebra 2 Introduction - Basic Review lesson
2.  Solving Linear Equations With Variables, Parentheses and Fractions
3.  Solving and Graphing Inequalities on a Number line
4  Solving Absolute Value Equations With Inequalities
5.  Calculating the Slope Between Two Points With Fractions
6.  Writing Linear Equations In Slope Intercept Form, Point Slope Form, and Standard Form
7.  Parallel and Perpendicular Lines
8.  Rate of Change Problems - Formula & Calculations
9.  Graphing Linear Equations Using the Slope and Y Intercept 
10.  Graphing Linear Equations Using X and Y Intercepts
11.  Horizontal and Vertical Lines
12.  Graphing Absolute Value Equations 
13.  Parent Functions and Transformations
14.  Systems of Equations - Substitution, Elimination and Graphically - Point of Intersection
15.  Horizontal and Vertical Shifts - Reflection about X and Y axis
16. Factoring Binomials - Difference of Perfect Squares Method
17.  Factoring Trinomials - Leading Coefficient
18.  Factoring By Grouping and GCF Method
19.  Factoring Polynomials - Cubic and With Synthetic Division
20.  Solving Quadratic Equations By Factoring
21.  Solving Quadratic Equations By Completing The Square
22.  Factoring Quadratic Expressions Using the Quadratic Formula
23.  Graphing Quadratic Equations In Standard and Vertex Form
24.  Vertex, Axis of Symmetry, Maximum and Minimum Values
25.  Domain and Range of Linear, Absolute Value and Quadratic Equations - Interval Notation
26.  Discriminant Formula - Real Solutions vs Imaginary Solutions
27.  Imaginary Numbers - Adding, Subtracting, Multiplying, Dividing and Simplifying
28.  Graphing Complex Numbers - Absolute Value Calculation
29.  Exponent Properties - Multiplying and Dividing
30.  Negative Exponents - Simplifying
31.  Zeros of Polynomial Functions
32.  List of Possible Rational Zeros
33.  Synthetic Division and Long Division
34.  Factoring Cubic Polynomials Using Synthetic Division and Factoring By Grouping
35.  Evaluating Functions Using Synthetic Division
36.  Inverse Functions 
37.  Composite Functions - F(g(x))
38.  Evaluating Logarithmic Functions
39.  Properties of Logarithms
40.  Condensing, Expanding and Solving Logarithmic Equations
41.  Simplifying Radical Expressions and Solving Radical Equations
42.  Graphing Square Root / Radical Equations With Transformation - Domain and Range
43.  Simplifying Rational Expressions and Solving Rational Equations
44.  Rational Expressions - Adding, Subtracting, Multiplying and Dividing
45.  Rationalizing the Denominator
46.  Graphing Rational Equations
47.  Horizontal and Vertical Asymptotes Plus Holes

Disclaimer:  Some of the links associated with this video may generate affiliate commissions on my behalf.  As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.

#algebra 

Algebra 2 Introduction, Basic Review, Factoring, Slope, Absolute Value, Linear, Quadratic Equations

SAT Math Test Prep Online Crash Course Algebra & Geometry Study Guide Review

This online sat math test prep review youtube video tutorial will help you to learn the fundamentals behind the main concepts that are routinely covered on the scholastic aptitude test.  This online crash course video contains plenty of examples and practice problems for you work on including very hard / difficult math questions with answers and solutions included.  There are six main lessons in this study guide that are accompanied by a review of the most important topics, concepts, equations and formulas that you need to do well on the sat.  This video contains plenty of multiple choice problems that you can work on as a practice test.


Topics include:
1.  Evaluating composite functions and algebraic expressions
2.  Solving equations and finding the value of x – SAT Math Algebra Review
3.  Simplifying Radicals, Exponents, and Factoring Trinomials
4.  Solving Equations With Two Variables Using The Substitution and Elimination Method
5.  Absolute Value Equations and Multivariable Functions
6.  How To Convert Sentences Into Equations to Solve SAT Math Word Problems
7.  Word Problems With Averages and Total Sum
8.  Consecutive Even / Odd Positive or Negative Integer Word Problem
9.  Basketball Team Word Problems – Games won vs Lost
10.  Past Present Future Age Word Problem
11.  Inclusive vs Exclusive Numbers In a List
12.  Distance Rate Time SAT Math Word Problems
13.  Ratios and Proportions Based Word Problems
14.  Red Green Blue Yellow Marble Probability Problem
15.  Nickels Dimes Quarters Word Problem
16.  Number of Workers SAT word problem
17.  Permutations Combinations and Fundamental Counting Principle
18.  Two or Three Digit Integer Word Problem
19.  Average Score, Arithmetic Mean, and Weighted Average SAT Math Problem
20.  Percent Increase or Decrease Word Problem – Sales Tax vs Discount
21.  Original Selling Price and Percent Change Practice Problems
22.  Percentage Problems with x and y Variables
23.  Slope Calculations, Midpoint and Distance Formula
24.  Mean, Median, Mode, and Range
25.  Arithmetic and Geometric Series and Sequences Word Problems
26.  Linear, Quadratic, and Absolute Value Functions and Graphs
27.  SAT Math Geometry Review
28.  How to Find the Side Length of a Triangle Given Area and Height
29.  How to Calculate the Perimeter of a Triangle Given Hypotenuse
30.  How to Determine the Area of a Right Triangle
31.  Calculating the Area of a Parallelogram
32.  Percent Increase or Decrease of Radius and Height of a Cylinder – Effect on Volume
33.  How to Calculate the Perimeter of a Square Given It’s Diagonal
34.  Calculating the Altitude of a 45 45 90 degree right triangle
35.  Finding the Perimeter of an Equilateral or Equiangular Triangle
36.  Calculating the Sum of the Three Remote Exterior Angles of a Triangle
37.  Segment Midpoint Geometry Problems
38.  Parallel Lines – Corresponding, Alternate Interior, Exterior and Vertical Angles
39.  Linear Pairs – Supplementary and Complementary Angles
40.  Finding the area of the shaded region of a circle
41.  Tangent and Secant Lines on Circles
42.  How to Calculate the Arc of a segment of a circle
43.  Rectangle Semicircle Word Problem
44.  How to Calculate the Perimeter of a Rhombus Given It’s Side Length
45.  How to Determine the altitude of a right triangle using the geometric mean and proportions

Disclaimer:  Some of the links associated with this video may generate affiliate commissions on my behalf should you decide to make a purchase through such websites.

#algebra 

SAT Math Test Prep Online Crash Course Algebra & Geometry Study Guide Review

Algebra Course: Fundamental Theorem of Algebra

This math video tutorial provides a basic introduction into the Fundamental Theorem of Algebra which states that a polynomial function of degreen n has exactly n roots provided that n is equal to or greater than 1.

#algebra 

Algebra Course: Fundamental Theorem of Algebra

Algebra Course: Systems of Quadratic Equations

This video tutorial explains how to solve a system of two quadratic equations by substitution and by graphing.

#algebra 

Algebra Course: Systems of Quadratic Equations

Greek Alphabet Symbols List - College Math, Chemistry, & Physics

This video provides a list of symbols found in the Greek Alphabet that are typically used in equations and formulas found in chemistry, physics, and college math courses like college algebra, geometry, trigonometry, precalculus, and calculus.

#algebra 

Greek Alphabet Symbols List - College Math, Chemistry, & Physics

Algebra Course: Introduction to Statistics

This video tutorial provides a basic introduction into statistics.  It explains how to find the mean, median, mode, and range of a data set.  It also explains how to find the interquartile range, quartiles, percentiles as well as any outliers.  The full version of this video which can be found on my patreon page also mentions how to construct box and whisker plots, histograms, frequency tables, frequency distribution tables, dot plots, and stem and leaf plots.  It also covers relative frequency and cumulative relative frequency as well as how to use it to determine the value that a corresponds to a certain percentile.  Finally, this video also discusses skewness - it explains which distribution is symmetric and which is skewed to the right (positive skew) and which is skewed to the left (negative skew).

#algebra 

Algebra Course: Introduction to Statistics

Álgebra Lineal Para Saber Para El Aprendizaje Automático

En este artículo, aprenderemos sobre Álgebra Lineal. El Álgebra Lineal es la columna vertebral de la Inteligencia Artificial. Los modelos complejos en Machine Learning se representan y resuelven con los procesos de Álgebra Lineal y, por lo tanto, es crítico. Todos y cada uno de los ingenieros de aprendizaje automático deben tener una base sólida.

Lea el artículo anterior:  ¿Por qué los ingenieros de IA necesitan cálculo  para profundizar en el cálculo y convertirse en un mejor ingeniero de IA?

Álgebra lineal

El álgebra lineal trata con ecuaciones lineales como mapas lineales (que es un mapeo de dos espacios vectoriales diferentes que conservan la operación vectorial de suma y multiplicación escalar) y sus representaciones en espacios vectoriales y mediante matrices. El álgebra lineal es clave en casi todas las áreas de las matemáticas, ya que se usa ampliamente en la ciencia y en muchos campos de la ingeniería, ya que ayuda a modelar diferentes fenómenos naturales y calcularlos de manera eficiente. El álgebra lineal es muy similar al álgebra de la que hablamos en nuestro artículo anterior, excepto que en lugar de números simples ordinarios, se trata de vectores. Muchas de las mismas operaciones algebraicas que hemos usado para realizar en números ordinarios (es decir, escalares), como la suma, la resta y la multiplicación, pueden generalizarse para operar en vectores.


Lo que aprenderemos en este artículo es, en general, lo que sucede cuando tenemos múltiples variables,

  • Introducción a los vectores
  • Resolver conjuntos de ecuaciones lineales
  • Introducción a las matrices
  • Resolver conjuntos de ecuaciones lineales de matrices
  • Transformaciones lineales
  • Matriz de identidad
  • Determinante

Vectores

Un vector es una lista de números. Hay (al menos) dos formas de interpretar lo que significa esta lista de números: Una forma de pensar en el vector como un punto en el espacio. Si es así, esta lista de números diferentes sería de hecho una forma de identificar ese mismo punto en el espacio de modo que cada número represente el componente del vector de esa dimensión. Otro enfoque para comprender el vector es como una magnitud y una dirección, por ejemplo, una cantidad como una velocidad ("la velocidad del automóvil es de 120 mph de norte a noreste").

Suma de vectores

Los vectores se pueden sumar y restar.

Gráficamente, podemos imaginar la suma de dos vectores diferentes como la colocación de dos segmentos de línea de extremo a extremo, manteniendo la distancia y la dirección. Un ejemplo de esto se ilustra a continuación, mostrando la suma de dos vectores que crean el tercer vector. Un vector se denota por su nombre con una flecha sobre él.

Dejar,

Álgebra lineal para saber para el aprendizaje automático,Álgebra lineal para saber para el aprendizaje automático 

Sumando los vectores, obtenemos,

Álgebra lineal para saber para el aprendizaje automáticoÁlgebra lineal para saber para el aprendizaje automáticoÁlgebra lineal para saber para el aprendizaje automático 

Este vector resultante sería el tercer vector.

Multiplicación de vectores

Hay dos formas distinguibles diferentes de multiplicar vectores, que se denominan productos escalares (es decir, productos escalares) y productos cruzados. El producto escalar genera un valor escalar a partir del producto de dos vectores y se analizará con más detalle a continuación. No confundas el producto punto con el producto cruz que es completamente diferente.

Aquí,

Álgebra lineal para saber para el aprendizaje automáticoÁlgebra lineal para saber para el aprendizaje automáticoÁlgebra lineal para saber para el aprendizaje automático

Y los cálculos son los mismos en múltiples dimensiones.

Resolviendo un conjunto de ecuaciones,

Una de las formas de resolver las dos ecuaciones es dibujarlas gráficamente y cómo se intersecan entre sí.

En Álgebra Lineal, tomamos las matrices y las resolvemos.

Tomemos, dos ecuaciones,

X = Y + 5

3X + 2Y = 5

Tomando tanto X como Y en los mismos lados, obtenemos,

X-Y = 5

3X + 2 Y = 5

Tomando la ecuación anterior, I y II en forma matricial, obtenemos, 

Álgebra lineal para saber para el aprendizaje automáticoÁlgebra lineal para saber para el aprendizaje automáticoÁlgebra lineal para saber para el aprendizaje automático

Si desea obtener más información sobre el álgebra lineal, consulte este increíble video de AI 42

Matriz

Una matriz, al igual que un vector, también puede entenderse como una colección de números. La principal diferencia entre el vector y la matriz es que la matriz es una tabla de números en lugar de una lista.

Fila de matriz y columna de matriz

Las entradas o elementos son diferentes números, símbolos y expresiones en una matriz. Filas y Columnas son las líneas horizontales y verticales en una matriz respectivamente.

Multiplicación de matrices

La multiplicación de matrices es complicada, ya que múltiples elementos en la primera matriz interactúan con múltiples elementos en la segunda para producir cada elemento en la matriz del producto. Esto explica cómo la multiplicación de matrices puede ser una tarea mundana para llevar a cabo a mano y, por lo tanto, llevaría mucho tiempo en una computadora para matrices muy grandes.

Tomando la multiplicación de matrices para dos ecuaciones diferentes,

X-Y = 5

3X + 2 Y = 5 se puede escribir como,

Álgebra lineal para saber para el aprendizaje automáticoÁlgebra lineal para saber para el aprendizaje automáticoÁlgebra lineal para saber para el aprendizaje automático

 

Aquí, los valores verticales 1, 3 y –1,2 son columnas y los horizontales se toman como filas.

Transformación lineal

Una Transformación Lineal se puede definir como una función de un espacio vectorial a otro que mantiene la estructura lineal de cada espacio vectorial. También se le llama operador lineal o mapa.

La matriz,

Álgebra lineal para saber para el aprendizaje automático

describe una transformación lineal.

Determinante

El determinante se puede definir como un valor escalar que describe ciertas propiedades de la transformación lineal descrita por la matriz.

Para, A = = det (A) = 1*2 – 3* (-1) = 2+3 = 5

Matriz de identidad

Una matriz identidad es una matriz cuadrada dada de cualquier orden que contiene sus principales elementos diagonales con un valor de uno, mientras que el resto de los elementos de la matriz son iguales a cero.

El producto de cada matriz cuadrada y el de su matriz identidad siempre daría como resultado la matriz original, sin importar el orden en que se operara la multiplicación.

Álgebra lineal para saber para el aprendizaje automático= detÁlgebra lineal para saber para el aprendizaje automático= 1*1 – 0*0 = 1

Transposición de matriz

La transposición de matriz, es decir, la transposición de cualquier matriz daría como resultado una nueva matriz donde las filas de la matriz anterior se convierten en su columna. El superíndice 'T' significa 'transponer' para la matriz.

Álgebra lineal para saber para el aprendizaje automáticoÁlgebra lineal para saber para el aprendizaje automático

Soluciones de mínimos cuadrados

El proceso de mínimos cuadrados es un enfoque estándar en el análisis de regresión para aproximar la solución de diferentes conjuntos de ecuaciones que contienen más ecuaciones que incógnitas (también conocidas como sistemas sobredeterminados) al reducir la suma de los cuadrados de los residuos hechos en el resultados de cada ecuación,

  • ¿Qué pasa si Ax = b no tiene solución? ¿Cuál es la mejor solución aproximada?

La mejor solución aproximada es lo que llamamos solución de mínimos cuadrados.

Cada uno de los puntos tiene coordenadas para ello. Ej. (x1, y1), (x2, y2)… (xn, yn) al azar. Habría una línea que se puede dibujar uniendo el punto más alto ahora en una línea recta. Esta línea significaría la solución de mínimos cuadrados.

¿Dónde se usa el mínimo cuadrado en el aprendizaje automático?

Reconocimiento de imagen

El reconocimiento de imágenes es un subconjunto de la visión por computadora y la inteligencia artificial, que representa un conjunto de procesos para detectar y analizar imágenes con el fin de permitir la automatización de una tarea específica en particular. Es una tecnología que es capaz de reconocer diferentes ubicaciones, personas, objetos y muchos otros tipos de elementos dentro de una imagen y sacar conclusiones de ellos mediante el análisis.

Tomemos a, a. Imagen de 10 X 10 píxeles b. Valores de matriz de la imagen para 1 por cada píxel punteado.

Si tuviéramos que dibujar un círculo, la matriz tendría valores 0 en todos los demás lugares que no se usarían para indicar la parte del círculo y 1 para los píxeles donde estaría el dibujo del círculo.

Este proceso de transformación se utiliza para detectar objetos y análisis de características en el reconocimiento de imágenes.

¿Cómo ML hace la transformación lineal y la conecta con la matriz?

Cuando estamos tratando de ajustar el modelo, estamos tratando de encontrar la matriz de transformación y la mejor solución. Esto se hace en varios niveles. En primer lugar, la transformación se realiza para que los bordes se hagan visibles. Después de eso, se definen modelos para diferenciar entre múltiples objetos, para egcat y dog. Y después, se realizan muchas capas de transformaciones seguidas para hacer el trabajo.

Conclusión

En este artículo aprendimos sobre el Álgebra Lineal que es una de las ramas más importantes de las matemáticas sin la cual sería imposible resolver problemas complejos a través de la Inteligencia Artificial. Aprendimos sobre vectores: suma y multiplicación, resolvimos ecuaciones lineales, entendimos sobre matrices y también las resolvimos con ecuaciones lineales, profundizamos en la transformación lineal, la matriz de identidad y el proceso para calcular valores determinantes. También aprendimos a transponer matrices y comprendimos el concepto de solución de mínimos cuadrados. Todos estos diferentes aspectos del álgebra lineal lo ayudarán a convertirse en un mejor ingeniero de aprendizaje automático.

Fuente: https://www.c-sharpcorner.com/article/linear-algebra-to-know-for-machine-learning/ 

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Álgebra Lineal Para Saber Para El Aprendizaje Automático

Algebra Course: ACT Math Test Prep

This ACT math prep study guide review youtube video tutorial contains plenty of examples and practice problems with solutions to help you master the concepts that is commonly tested on the act.  It contains tips and strategies to help you some common act math problems in algebra, geometry, and trigonometry.  This video contains the formulas you need to answer very common questions.  This video provides a basic overview of questions you might see on the actual test.  If you need help, you came to the right place.

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Algebra Course: ACT Math Test Prep