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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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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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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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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