Symmetric Matrices and SVD Decomposition

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Linear Algebra: Singular Value Decomposition

Delves into singular value decomposition and its applications in linear algebra.

Symmetric Matrices: Properties and Decomposition

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

Balanced Realization: SISO Case

Covers the concept of balanced realization in the SISO case, focusing on system observability and controllability.

Spectral Theorem Recap

Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.

Convergence Rate Theorem: Part 1

Delves into the proof of the convergence rate theorem for an ergodic Markov chain, emphasizing eigenvalues and detailed balance properties.

Diagonalization of Symmetric Matrices

Explores the diagonalization of symmetric matrices and the orthogonality of eigenvectors.

Singular Value Decomposition

Covers the Singular Value Decomposition theorem and its application in decomposing matrices.

Canonical Correlation Analysis: Overview

Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.

Calcul de valeurs propres

Covers the calculation of eigenvalues and eigenvectors, emphasizing their significance and applications.

Coxeter Groups: Spectral Theorem and Sylvester's Criterion

Explores the spectral theorem, Coxeter graphs, eigenvalues, and determinants of positive definite matrices.