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Workbook 23

Chapter 1: 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

• projections (Missing reference)
• Define a unit vector from Chapter 5: "Vectors" in Workbook 06

Chapter 2: Singular Value Decomposition

PDF

Downloads

• Python script for SVD calculations

Objectives

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

• Video: SVD Visualized, Singular Value Decomposition explained | SEE Matrix , Chapter 3 #SoME2 - YouTube
• Video: Singular Value Decomposition (the SVD) - YouTube
• Video: What is the Singular Value Decomposition? - YouTube
• Reference: AMS :: Feature Column from the AMS

Prerequisites

• Understand how to compute eigenvalues and eigenvectors from Chapter 6: "Eigenvectors and Eigenvalues" in Workbook 22

Chapter 3: Tackling Difficult Problems: Positive Semidefinite Matrices

PDF

Objectives

Understand how to calculate positive semidefinite values

• Video: 5. Positive Definite and Semidefinite Matrices - YouTube
• Video: What Does It Mean For a Matrix to be POSITIVE? The Practical Guide to Semidefinite Programming(1/4) - YouTube
• Video: 25. Symmetric Matrices and Positive Definiteness - YouTube
• Video: Symmetric Matrices and Positive Definiteness - YouTube
• Reference: Positive semidefinite - Wikipedia

Prerequisites

• Understand how to add, subtract, and multiplication matrices from Chapter 2: "Vectors and Matrices" in Workbook 21
• Understand matrices, vector representations of matrices, dimensions of matrices, scalar matrix multiplication, and the zero matrix and identity matix. from Chapter 2: "Vectors and Matrices" in Workbook 21

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