Eigenvalues and Eigenvectors of Markov Chains

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

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Covers the diagonalization of symmetric matrices, the spectral theorem, and the use of spectral decomposition.

Diagonalization in Symmetric Matrices

Explores diagonalization in symmetric matrices, emphasizing orthogonality and orthonormal bases.

Spectral Theorem Recap

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

Symmetric Matrices: Properties and Decomposition

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

Diagonalization of Matrices

Explains the diagonalization of matrices, criteria, and significance of distinct eigenvalues.

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Explores the complexity of matrix computations, focusing on eigenvalues and eigenvectors of symmetric matrices and the challenges in computing them.

Matrix Eigenvalues and Eigenvectors

Explains how the inverse of a matrix shares its eigenvalue and how the transposed version has the same set of eigenvalues.

Eigenvalues and Optimization: Numerical Analysis Techniques

Discusses eigenvalues, their calculation methods, and their applications in optimization and numerical analysis.