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Tag: linear algebra

#009 The Singular Value Decomposition(SVD) – illustrated in Python

Highlight: In this post, we will talk about the Singular Value Decomposition (SVD). We will see that is the continuation of the Linear Algebra post about eigenvectors and eigenvalues. Well, it is probably one of the most important algorithms in Linear Algebra, math, and engineering. Applications are immense, starting from Image processing, Computer vision, up to industrial applications, such as Google rank algorithm. O.K., you probably heard about SVD already. So, let’s start! Tutorial Overview:…
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#007 Linear Algebra – Change of basis

Highlight: So far, we have already talked that it is possible to represent the vector using different basis vectors. In this post we will learn how to go from our standard coordinate system \(\left ( x,y \right ) \) into some other bases. Next, we will also learn why this change of basis can be very useful. For now, we will just say that it’s frequently applied in many signal processing and machine learning methods.…
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#006 Linear Algebra – Inner or Dot Product of two Vectors

Highlight: In this post we will review one of the fundamental operators in Linear Algebra. It is known as a Dot product or an Inner product of two vectors. Most of you are already familiar with this operator, and actually it’s quite easy to explain. And yet, we will give some additional insights as well as some basic info how to use it in Python. Tutorial Overview: Dot product :: Definition and properties Linear functions…
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#008 Linear Algebra – Eigenvectors and Eigenvalues

Highlight: In this post we will talk about eigenvalues and eigenvectors. This concept proved to be quite puzzling to comprehend for many machine learning and linear algebra practitioners. However, with a very good and solid introduction that we provided in our previous posts we will be able to explain eigenvalues and eigenvectors and enable very good visual interpretation and intuition of these topics. We give some Python recipes as well. Tutorial Overview: Intuition about eigenvectors…
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#005 Linear Algebra – Inverse matrices, Rank, Column space and Null space

Highlights: Hello and welcome back. In this post we will learn about some very important topics in linear algebra. They involve: Tutorial Overview: Inverse matrices Rank Span Null space 1. Inverse matrices The following concepts we will observe under the light of linear transformations. They will help us to gain intuition how we can solve linear equations and better understand some concepts related to linear transformations in general. Usually, when you first hear about linear…
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