Vern  Greenholt

Vern Greenholt

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.

Image for post

Figure 1

Image for post

Image for post

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.

Image for post

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

What is GEEK

Buddha Community

Eigen Theory From Scratch
Brielle  Maggio

Brielle Maggio

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

Download NodeJS
https://nodejs.org/en/download/

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

Kabanda  Nat

Kabanda Nat

1624633200

Using An Existing Blogging Platform vs Building A Blog From Scratch

Each option has its benefits and drawbacks. The purpose of this article is to answer this question and clarify it! Also, it’s important to note that everyone has different needs. So there is not a universal answer.
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

Vern  Greenholt

Vern Greenholt

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.

Image for post

Figure 1

Image for post

Image for post

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.

Image for post

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

rick william

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

Linda nano

Linda nano

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.
Cryptocurrency trading is VERY risky. Make sure you understand these risks and that you are responsible for what you do with your money
🔥 If you’re a beginner. I believe the article below will be useful to you ☞ What You Should Know Before Investing in Cryptocurrency - For Beginner
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Thanks for visiting and watching! Please don’t forget to leave a like, comment and share!

#bitcoin #blockchain #xrp news #$btc #xrp news - why xrp is number 1, a theory on how $xrp could dethrone $btc #theory on how $xrp