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Category: Linear Algebra

#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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#004 Linear Algebra – The determinant

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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#003 Linear Algebra – Linear transformations and matrices

Highlight: Hello and welcome back! This post will be quite an interesting one. We will show how a 2D plane can be transformed into another one. Understanding these concepts is a crucial step for some more advanced linear algebra/machine learning methods (e.g. SVD, PCA). So, let’s proceed and we will learn how to connect a matrix-vector multiplication with a linear transformation. Tutorial Overview: Linear transformation Linear transformation and basis vectors 2×2 Matrix as a linear…
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#002 Linear Algebra – Linear combination of Vectors

Highlights: In this post we are going to continue our story about vectors. We will talk more about basis vectors, linear combination of vectors and what is the span of vectors. We provide a code examples to demonstrate how to work with vectors in Python. Tutorial Overview: Basis vectors \(\hat{i}\) and \(\hat{j}\) Different basis vectors Linear combination of vectors What is a span of vectors? Linearly independent and dependent vectors 1. Basis vectors \(\hat{i}\) and…
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#001 Linear Algebra: Vector addition and scalar-vector multiplication

Highlights: In this post we are going to talk about vectors. They are the fundamental building blocks in Linear Algebra. We will give an intuitive definition what the vectors are, where we use them, how we add them and multiply with scalars. We provide a code examples to demonstrate how to work with vectors in Python. Tutorial Overview: What is a vector? Examples of vectors in Linear Algebra Definition of a vector Vector addition Scalar-vector…
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