Prerequisite material is overviewed in a series of videos that are available under the "Prerequisites" topic in the navigation bar, which is to the left of this text.

The lectures were produced using technology that is described in this video:
https://youtu.be/ltOxgb28ZKY

No.	PDF	Video
	Week   1
1	Class #01	Introduction To Linear Methods for AI
1a		Course Overview
2	Class #02	Eigenvalues, Eigenvectors
2a		Matrix Columns
2b		Eigenfacts
3	Class #03	Graphs: Adjacency Matrix and Laplacian Matrix
3a		Introduction To Graphs
3b		Relevant Definitions For Graphs
3c		The Adjacency Matrix
3d		Non-Bipartite Graphs
3e		The Degree Matrix
3f		A Laplacian Matrix
3g		Properties Of A Laplacian Matrix
3h		The Fiedler Vector
	Week   2
4	Class #04	Vector Spaces
4a		Introduction To Vector Spaces
4b		Block Partitioning A Matrix
4c		Vector-Space Properties
4d		The Column Space
4e		The Null Space
5	Class #05	Spanning Sets And Basis Vectors
5a		Introduction To Vector Spaces
5b		Relevant Definitions For Basis Vectors
5c		Basis Vectors For A Column Space
5d		Orthogonal Subspaces
6	Quiz #1	Matrix Properties and Vector Spaces
	Week   3
7	Class #07	Diagonalizable Matrices
7a		Similar Matrices
7b		Diagonalizability
7c		Examples of Diagonalizability
7d		The Matrix Square Root
8	Class #08	Spectral Decomposition and Positive [Semi-]Definite Matrices
8a		Real Normal Matrices
8b		Real Orthogonal Matrices
8c		Real Symmetric Matrices
8d		The Spectral Theorem
8e		Positive Definite Matrices
8f		The Quadratic Form
8g		Mean And Variance Of Data
8h		The Covariance Matrix
9	Test #1	Matrix Properties and Vector Spaces
	Week   4
10	Class #10	Design Matrix And Standardized Data
10a		Variables And Observations
10b		Variables As Vectors
10c		Zero-Mean Data
10d		Unit-Variance Data
10e		Standardized Data For Regression
10f		Measuring Standard Deviations
11	Class #11	Orthogonal Projection
11a		Concepts In Orthogonal Projection
11b		Projecting A Vector To A Vector
11c		Projecting A Vector To A Vector Space
11d		The Normal Equation
11e		Overdetermined Linear Equations
12	Class #12	Patterns - Linear Regression
12a		Concepts In Statistical Regression
12b		Concepts In Linear Regression
12c		Examples Of Linear Regression
12d		Data Standardization For Linear Regression
12e		Residual Error In Linear Regression
	Week   5
13	Class #13	Cross-Validating Linear Regression
13a		Validation Of Linear Regression
13b		Training Sets And Testing Sets
13c		K-Fold Cross-Validation Of Linear Regression
13d		Examples Of 5-Fold Cross-Validation
14	Class #14	Singular Value Decomposition, Or SVD
14a		Introduction To The SVD
14b		The Left-Transpose Product
14c		The Right-Transpose Product
14d		Structure Of The SVD
15	Quiz #2	Matrices and Linear Regression
	Week   6
16	Class #16	Orthonormal Basis Vectors And The SVD
16a		I Did Not Shoot The SVD
16b		Examples Of The SVD
16c		Matrix Spaces And The SVD
16d		The Null Space And The SVD
16e		Orthonormal Basis Vectors And The SVD
17	Class #17	Principal Components Analysis, Or PCA
17a		Introduction To PCA
17b		PCA From Covariance Matrix
17c		PCA As Spectral Decomposition
17d		Computing Data Scores Using PCA
17e		Matrix Norms
17f		L2 Matrix Norm And Frobenius Matrix Norm
17g		Matrix Series From The SVD
17f		Scree Plot Of Singular Values
18	Test #2	Matrices and Linear Regression
	Reading Week
		Holiday Special
	Week   7
19	Class #19	PCA - Algebra, Dimensionality Reduction
19a		Revisiting PCA
19b		The Scatter Matrix Of Variables For PCA
19c		PCA As Matrix Approximation
19d		PCA As Dimensionality Reduction
19e		Low-Rank Approximations
20	Class #20	Unsupervised Learning - K-Means Clustering
20a		A Conceptual Hierarchy Of Machine Learning
20b		Hyperplane of Separation
20c		Basics Of Vector Clustering
20d		A K-Means Clustering Algorithm
20e		Clustering The Iris Data
21	Quiz #3	The SVD, PCA, And Dimensionality Reduction
	Week   8
22	Class #22	Classification - Linear Separability
22a		Separating Two Clusters
22b		A Hyperplane From Cluster Centroids
22c		Hyperplanes For Multiple Clusters
22d		The Davies-Bouldin Index For Clusters
23	Class #23	Classification - Assessment With Confusion Matrix
23a		Data Labels As Dependent Variables
23b		Confusion Matrix For Binary Labels
23c		Example Of Confusion Matrix
24	Test #3	The SVD, PCA, And Dimensionality Reduction
	Week   9
25	Class #25	Classification - Assessment With ROC Curve
25a		Receiver Operator Characteristic, Or ROC
25b		ROC And The Confusion Matrix
25c		Example ROC Curve For Fictitious Virus
26	Class #26	Odds Of Occurrence And Probability
26a		Odds Of Hyperplane Classification
26b		Odds And Probability
26c		The Logistic Function For Odds
26d		Properties Of The Logistic Function
27	Quiz #4	Classification Assessment, Odds Of Occurrence
	Week   10
28	Class #28	Elementary Numerical Optimization
28a		Stationary Points
28b		Iteration With Steepest Descent
29	Class #29	Artificial Neuron - Learning Weights
29a		Artificial Neuron - Simple Model
29b		Data Flow And Computations For Neurons
29c		Hyperplane Separation For Neurons
29d		Steepest Descent For Artificial Neurons
29e		Hyperplane Classification Of Iris Data
30	Test #4	Classification Assessment, Odds Of Occurrence
	Week   11
31	Class #31	Classification - Logistic Regression
31a		Shortcomings Of Perceptrons
31b		Scores From Logistic Activation
31c		Residual Error Of Scores
31d		Logistic Regression For Iris Data
32	Class #32	Nonlinear Separation - Embeddings, Gram Matrix
32a		Some Data Are Nonlinearly Separable
32b		Embedding A Vector Space
32c		Gram Matrix For An Embedding
33	Class #33	Nonlinear Separation - Kernel PCA
33a		High-Dimensional PCA
33b		Scatter Matrix Of Observations
33c		Kernel PCA Using The Gram Matrix
33d		Kernel PCA For Iris Data
	Week   12
34	Class #34	Spectral Clustering Of Data
34a		Fiedler Vector And Spectral Decomposition
34b		Spectral Clustering Using Eigenvectors
34c		Distance Matrix And Spectral Clustering
35	Class #35	Course Summary
35a		Course Summary
		Unplanned Recording Events
	Extra Material
	Table of Contents
	References

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