Workbook 23

Chapter 1: Projections

PDF

Downloads

Python file for calculating vector projections.

Objectives

Understand vector projections, what they create, and how to calculate them using matrices

Video: Introduction to projections | Matrix transformations | Linear Algebra | Khan Academy - YouTube
Video: Calculus 3 - Vector Projections & Orthogonal Components - YouTube
Video: Vector Projections | Vector Calculus #17 - YouTube
Video: Dot products and duality | Chapter 9, Essence of linear algebra - YouTube
Video: 15. Projections onto Subspaces - YouTube
Video: Projection into Subspaces - YouTube
Video: The Math behind (most) 3D games - Perspective Projection - YouTube
Video: Vector Projections - YouTube
Video: Vector Projections Are Just Shadows - YouTube
Reference: Projection (linear algebra) - Wikipedia
Reference: Vector projection - Wikipedia
Reference: 2.6: The Vector Projection of One Vector onto Another - Mathematics LibreTexts
Reference: Scalar projection - Wikipedia

Prerequisites

Understand a vector and its properties in depth from Chapter 5: "Vectors" in Workbook 07
Understand and multiply vectors using the dot product from Chapter 2: "The Dot Product" in Workbook 11
Define a unit vector from Chapter 5: "Vectors" in Workbook 07

Chapter 2: The Gram-Schmidt Process

PDF

Downloads

Python program for the gram-schmidt normalization process

Objectives

Understand how to use the gram-schmidt process for vectors

Video: Gram-Schmidt Process in Space (Step-by-Step 3D Visual) - YouTube
Video: Gram-Schmidt Orthogonalization - YouTube
Video: Gram-Schmidt Orthogonalization (Proof and Example) | Linear Algebra - YouTube
Video: The Gram-Schmidt Process - YouTube
Video: Full example: using Gram-Schmidt - YouTube
Video: The Gram-Schmidt process | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy - YouTube
Reference: Gram Schmidt Process for ML - GeeksforGeeks
Reference: Gram–Schmidt process - Wikipedia
Reference: Orthogonal basis - Wikipedia

Prerequisites

Understand vector projections, what they create, and how to calculate them using matrices from Chapter 1: "Projections" in Workbook 23
Define a unit vector from Chapter 5: "Vectors" in Workbook 07

Chapter 3: Eigenvectors and Eigenvalues

PDF

Downloads

Python script for creating and using eigenvalues and vectors.

Objectives

Understand how to compute eigenvalues and eigenvectors

Prerequisites

Understand a vector and its properties in depth from Chapter 5: "Vectors" in Workbook 07
Be able to find the determinant and understand what different values of it mean from Chapter 2: "Span" in Workbook 22
Understand linear combinations of vectors. from Chapter 4: "Linear Combinations of Vectors" in Workbook 21
Understand and multiply vectors using the dot product from Chapter 2: "The Dot Product" in Workbook 11

Chapter 4: Singular Value Decomposition

PDF

Downloads

Python script for SVD calculations

Objectives

Understand how to use SVD in both in mathematics and python.

Prerequisites

Understand how to compute eigenvalues and eigenvectors from Chapter 3: "Eigenvectors and Eigenvalues" in Workbook 23

Chapter 5: Tackling Difficult Problems: Positive Semidefinite Matrices

PDF

Objectives

Understand how to calculate positive semidefinite values

Prerequisites

Understand how to add, subtract, and multiplication matrices from Chapter 3: "Vectors and Matrices" in Workbook 21
Understand matrices, vector representations of matrices, dimensions of matrices, matrix multiplication from Chapter 3: "Vectors and Matrices" in Workbook 21

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