Coxeter Groups: Spectral Theorem and Sylvester's Criterion

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Covers non-negative definite matrices, covariance matrices, and Principal Component Analysis for optimal dimension reduction.

Explores the diagonalization of symmetric matrices through orthogonal decomposition and the spectral theorem.

Covers the spectral theorem, focusing on the second part and orthonormal sequences in a separable Hilbert space.

Introduces Convex Optimization notation, convex functions, vector norms, and matrix properties.

Explores the equivalence conditions for orthogonal matrices and includes examples of rotations.

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Explores spectral decomposition of symmetric matrices and Singular Value Decomposition (SVD) for matrix decomposition.

Covers examples of symmetric matrices and their properties, including eigenvectors and eigenvalues.

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