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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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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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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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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Highlight: In this post we will explain what the determinant is and why we use it in linear algebra. We will give an interpretation of a determinant both in a 2-D and in a 3-D space. Also, we will show how to implement these calculations in Python. Tutorial Overview: Determinant in a 2-D coordinate system Determinant in a 3-D coordinate system 1. Determinant in a 2-D coordinate system In the previous post we saw how…
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