 1598049780

# Eigen Theory From Scratch

In machine learning and data science, we often use the Eigen theory. It is widely used in the data dimensionality reduction technique; PCA. Also, even Google’s search algorithm ‘PageRank’ is based on this concept. Once you read this article you will be able to understand what exactly the Eigen theory is and how it can be used to solve problems.

In linear algebra, we can represent an object with combinations of multiple vectors. When we apply any kind of transformation on an object, we shall observe its impact on all the vectors.

When a transformation is applied, some vectors end up staying in the same position. These vectors are called eigenvectors. The factor by which eigenvectors are scaled after the transformation is called eigenvalues.

Now let us understand this with an example of a square shown below(figure1). Although the square is made up of millions of vectors, for our ease of understanding we consider only 3 vectors r, s, v. Vector r, s, v are on plane1, plane3, plane2 respectively. Figure 1  Transformation Matrix A

We apply transformation and let A be our transformation matrix.

Let’s have a very quick overview of what exactly the transformation matrix is.

When vector(s) are represented by a matrix, it must be read column-wise to identify vector(s).

Now, let’s see what exactly our transformation matrix A is doing to vector s. The x coordinate of vector s is 1 and the **y-**coordinate is also 1. (Make sure you are reading matrix A column-wise!)

When transformation matrix A is applied, x coordinate of s will move 1 unit in the x-direction and 0 unit in y-direction whereas y cordinate of s will move 0 unit in the x-direction and 2 unit in the y-direction. Transformation of vector s

So, we can see that after transformation coordinates of **s**are (1, 2).

The same transformation we apply to all the vector r, s, and v. Once the transformation is applied, our new coordinates are (0, 2), (1, 2), and (1, 0) respectively.

#data-science #machine-learning #mathematics #linear-algebra #eigenvectors #deep learning

## Buddha Community  1626657482

## Learn Angular From Scratch - Build SPA/Website with Angular 9 and Bootstrap - Part 1

Part 1 - Creating Angular 9 website using Angular CLI - Angular Single page application

Install Angular CLI
https://cli.angular.io/

Create Angular project from scratch using Angular CLI
ng new ProjectName

Spin up the application in the browser
ng serve -o

#angular #bootstrap #angular 9 #scratch #scratch 1624633200

## Using An Existing Blogging Platform vs Building A Blog From Scratch

What matters most
Before going further, let’s see the most important things one should look for when opening a blog. They are as follows:

• Having a personal domain - Having your domain is essential for two reasons. First of all, your blog looks more professional. Secondly, all the SEO benefits go to YOU. Hashnode is the only blogging platform that allows you to use your domain and for free. If you decide to move away, you retain all the SEO benefits, unlike other blogging platforms.

#scratch #existing blogging platform #a blog from scratch 1598049780

## Eigen Theory From Scratch

In machine learning and data science, we often use the Eigen theory. It is widely used in the data dimensionality reduction technique; PCA. Also, even Google’s search algorithm ‘PageRank’ is based on this concept. Once you read this article you will be able to understand what exactly the Eigen theory is and how it can be used to solve problems.

In linear algebra, we can represent an object with combinations of multiple vectors. When we apply any kind of transformation on an object, we shall observe its impact on all the vectors.

When a transformation is applied, some vectors end up staying in the same position. These vectors are called eigenvectors. The factor by which eigenvectors are scaled after the transformation is called eigenvalues.

Now let us understand this with an example of a square shown below(figure1). Although the square is made up of millions of vectors, for our ease of understanding we consider only 3 vectors r, s, v. Vector r, s, v are on plane1, plane3, plane2 respectively. Figure 1  Transformation Matrix A

We apply transformation and let A be our transformation matrix.

Let’s have a very quick overview of what exactly the transformation matrix is.

When vector(s) are represented by a matrix, it must be read column-wise to identify vector(s).

Now, let’s see what exactly our transformation matrix A is doing to vector s. The x coordinate of vector s is 1 and the **y-**coordinate is also 1. (Make sure you are reading matrix A column-wise!)

When transformation matrix A is applied, x coordinate of s will move 1 unit in the x-direction and 0 unit in y-direction whereas y cordinate of s will move 0 unit in the x-direction and 2 unit in the y-direction. Transformation of vector s

So, we can see that after transformation coordinates of **s**are (1, 2).

The same transformation we apply to all the vector r, s, and v. Once the transformation is applied, our new coordinates are (0, 2), (1, 2), and (1, 0) respectively.

#data-science #machine-learning #mathematics #linear-algebra #eigenvectors #deep learning

1622088103

## MAGENTO 2 SCRATCH COUPON CARD

Customers can scratch coupon card with the movement to win tempting discounts and get using promocode. Magento 2 Scratch coupon card extension helps to increase website use usability by engaged customers to the store. This extension helps to increase site traffic, website functionality.

#magento 2 scratch coupon card #scratch coupon card #magento 2 1624579200

## #XRP news - WHY XRP IS NUMBER 1, A Theory on how \$XRP could DETHRONE \$BTC

The Environmental Impact: Cryptocurrency Mining vs. Consensus. Why XRP will be a future king in this space, the most power efficient and scalable crypto currency ever created!

📺 The video in this post was made by Crypto 2103
The origin of the article: https://www.youtube.com/watch?v=-AAcyKoXrkI
🔺 DISCLAIMER: The article is for information sharing. The content of this video is solely the opinions of the speaker who is not a licensed financial advisor or registered investment advisor. Not investment advice or legal advice.
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