NumPy Linear Algebra and Matrix Functions

NumPy has a separate module for linear algebra. The module contains all the functions necessary for linear algebra. numpy.linalg is the package in NumPy for NumPy Linear Algebra. Linear Algebra is the branch of mathematics concerned with vector spaces and mapping amongst the spaces.

NumPy Linear Algebra

NumPy Linear Algebra

Let us see various Matrix and Vector Products in NumPy:

Matrix and Vector Products

For matrix and vector computations it has the following functions:

  • dot()- it can calculate the dot product of two arrays
  • vdot()- it can calculate the dot product of two vectors
  • inner()- it can calculate the inner product of arrays
  • outer()- it can compute the outer products of two arrays
  • matmul()- it can determine the matrix multiplication of two arrays
  • det()- it can calculate determinant of a matrix
  • solve()- it can solve linear matrix equation
  • inv()- it can calculate the multiplicative inverse of the matrix
  • trace()- it calculates the sum of diagonal elements
  • rank()- it returns the rank of the matrix

NumPy dot and vdot functions

The dot function gives the dot product of two matrices. It is similar to matrix multiplication.

The vdot function, on the other hand, is used for the dot product of two or more vectors. It is equivalent to the sum of the array elements.

#numpy tutorials #numpy eigenvalue functions #numpy

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NumPy Linear Algebra and Matrix Functions
Bailee  Streich

Bailee Streich

1619660285

Linear Algebra for Data Scientists with NumPy - Analytics India Magazine

A geek in Machine Learning with a Master’s degree in…

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Delhivery Promises To Fly Charters With Oxygen Concentrators In India

NumPy is an essential Python library to perform mathematical and scientific computations. NumPy offers Python’s array-like data structures with exclusive operations and methods. Many data science libraries and frameworks, including PandasScikit-Learn, Statsmodels, Matplotlib and SciPy, are built on top of NumPy with Numpy arrays in their building blocks. Some frameworks, including TensorFlow and PyTorch, introduce NumPy arrays or NumPy-alike arrays as their fundamental data structure in the name of tensors.

NumPy in data scienceHow NumPy becomes the base of Data Science computing system (source)

Data Science relies heavily on Linear Algebra. NumPy is famous for its Linear Algebra operations. This article discusses methods available in the NumPy library to perform various Linear Algebra operations with examples. These examples assume that the readers have a basic understanding of NumPy arrays. Check out the following articles to have a better understanding of NumPy fundamentals:

  1. Fundamental Concepts of NumPy
  2. Basic Programming with NumPy
  3. Top Resources to Learn NumPy

#developers corner #linear algebra #matrices #numpy #numpy array #numpy dot product #numpy matrix multiplication #numpy tutorial #svd #vectors

Bailee  Streich

Bailee Streich

1624447260

Course Review: Python for Linear Algebra

Because I am continuously endeavouring to improve my knowledge and skill of the Python programming language, I decided to take some free courses in an attempt to improve upon my knowledge base. I found one such course on linear algebra, which I found on YouTube. I decided to watch the video and undertake the course work because it focused on the Python programming language, something that I wanted to improve my skill in. Youtube video this course review was taken from:- (4) Python for linear algebra (for absolute beginners) — YouTube

The course is for absolute beginners, which is good because I have never studied linear algebra and had no idea what the terms I would be working with were.

Linear algebra is the branch of mathematics concerning linear equations, such as linear maps and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics.

Whilst studying linear algebra, I have learned a few topics that I had not previously known. For example:-

A scalar is simply a number, being an integer or a float. Scalers are convenient in applications that don’t need to be concerned with all the ways that data can be represented in a computer.

A vector is a one dimensional array of numbers. The difference between a vector is that it is mutable, being known as dynamic arrays.

A matrix is similar to a two dimensional rectangular array of data stored in rows and columns. The data stored in the matrix can be strings, numbers, etcetera.

In addition to the basic components of linear algebra, being a scalar, vector and matrix, there are several ways the vectors and matrix can be manipulated to make it suitable for machine learning.

I used Google Colab to code the programming examples and the assignments that were given in the 1 hour 51 minute video. It took a while to get into writing the code of the various subjects that were studied because, as the video stated, it is a course for absolute beginners.

The two main libraries that were used for this course were numpy and matplotlib. Numpy is the library that is used to carry out algebraic operations and matplotlib is used to graphically plot the points that are created in the program.

#numpy #matplotlib #python #linear-algebra #course review: python for linear algebra #linear algebra

NumPy Linear Algebra and Matrix Functions

NumPy has a separate module for linear algebra. The module contains all the functions necessary for linear algebra. numpy.linalg is the package in NumPy for NumPy Linear Algebra. Linear Algebra is the branch of mathematics concerned with vector spaces and mapping amongst the spaces.

NumPy Linear Algebra

NumPy Linear Algebra

Let us see various Matrix and Vector Products in NumPy:

Matrix and Vector Products

For matrix and vector computations it has the following functions:

  • dot()- it can calculate the dot product of two arrays
  • vdot()- it can calculate the dot product of two vectors
  • inner()- it can calculate the inner product of arrays
  • outer()- it can compute the outer products of two arrays
  • matmul()- it can determine the matrix multiplication of two arrays
  • det()- it can calculate determinant of a matrix
  • solve()- it can solve linear matrix equation
  • inv()- it can calculate the multiplicative inverse of the matrix
  • trace()- it calculates the sum of diagonal elements
  • rank()- it returns the rank of the matrix

NumPy dot and vdot functions

The dot function gives the dot product of two matrices. It is similar to matrix multiplication.

The vdot function, on the other hand, is used for the dot product of two or more vectors. It is equivalent to the sum of the array elements.

#numpy tutorials #numpy eigenvalue functions #numpy

NumPy Features - Why we should use Numpy?

Welcome to DataFlair!!! In this tutorial, we will learn Numpy Features and its importance.

NumPy is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays

NumPy (Numerical Python) is an open-source core Python library for scientific computations. It is a general-purpose array and matrices processing package. Python is slower as compared to Fortran and other languages to perform looping. To overcome this we use NumPy that converts monotonous code into the compiled form.

numpy features

NumPy Features

These are the important features of NumPy:

1. High-performance N-dimensional array object

This is the most important feature of the NumPy library. It is the homogeneous array object. We perform all the operations on the array elements. The arrays in NumPy can be one dimensional or multidimensional.

a. One dimensional array

The one-dimensional array is an array consisting of a single row or column. The elements of the array are of homogeneous nature.

b. Multidimensional array

In this case, we have various rows and columns. We consider each column as a dimension. The structure is similar to an excel sheet. The elements are homogenous.

2. It contains tools for integrating code from C/C++ and Fortran

We can use the functions in NumPy to work with code written in other languages. We can hence integrate the functionalities available in various programming languages. This helps implement inter-platform functions.

#numpy tutorials #features of numpy #numpy features #why use numpy #numpy

NumPy Applications - Uses of Numpy

In this Numpy tutorial, we will learn Numpy applications.

NumPy is a basic level external library in Python used for complex mathematical operations. NumPy overcomes slower executions with the use of multi-dimensional array objects. It has built-in functions for manipulating arrays. We can convert different algorithms to can into functions for applying on arrays.NumPy has applications that are not only limited to itself. It is a very diverse library and has a wide range of applications in other sectors. Numpy can be put to use along with Data Science, Data Analysis and Machine Learning. It is also a base for other python libraries. These libraries use the functionalities in NumPy to increase their capabilities.

numpy applications

Numpy Applications

1. An alternative for lists and arrays in Python

Arrays in Numpy are equivalent to lists in python. Like lists in python, the Numpy arrays are homogenous sets of elements. The most important feature of NumPy arrays is they are homogenous in nature. This differentiates them from python arrays. It maintains uniformity for mathematical operations that would not be possible with heterogeneous elements. Another benefit of using NumPy arrays is there are a large number of functions that are applicable to these arrays. These functions could not be performed when applied to python arrays due to their heterogeneous nature.

2. NumPy maintains minimal memory

Arrays in NumPy are objects. Python deletes and creates these objects continually, as per the requirements. Hence, the memory allocation is less as compared to Python lists. NumPy has features to avoid memory wastage in the data buffer. It consists of functions like copies, view, and indexing that helps in saving a lot of memory. Indexing helps to return the view of the original array, that implements reuse of the data. It also specifies the data type of the elements which leads to code optimization.

3. Using NumPy for multi-dimensional arrays

We can also create multi-dimensional arrays in NumPy.These arrays have multiple rows and columns. These arrays have more than one column that makes these multi-dimensional. Multi-dimensional array implements the creation of matrices. These matrices are easy to work with. With the use of matrices the code also becomes memory efficient. We have a matrix module to perform various operations on these matrices.

4. Mathematical operations with NumPy

Working with NumPy also includes easy to use functions for mathematical computations on the array data set. We have many modules for performing basic and special mathematical functions in NumPy. There are functions for Linear Algebra, bitwise operations, Fourier transform, arithmetic operations, string operations, etc.

#numpy tutorials #applications of numpy #numpy applications #uses of numpy #numpy