Lectures related to Symmetric Matrices and Eigenvalues

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Symmetric Matrices: Diagonalization

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Calcul de valeurs propres

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

Matrix Diagonalization: Spectral Theorem

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

Eigenvalues and Optimization: Numerical Analysis Techniques

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

Decomposition Spectral: Symmetric Matrices

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Symmetric Matrices: Properties and Decomposition

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

Symmetric Matrices: Eigenvalues and Eigenvectors

Explores the diagonalization of symmetric matrices using eigenvectors and eigenvalues, emphasizing orthogonality and real eigenvalues.

Symmetric Matrices: Diagonalizability and Eigenvectors

Explores the diagonalizability of symmetric matrices and their eigenvectors in an orthonormal basis.

Eigenvalues and Eigenvectors Decomposition

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

Diagonalization of Symmetric Matrices

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

Spectral Theorem Recap

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

Algebraic Multiplicity, Geometric Multiplicity

Explores algebraic and geometric multiplicities of eigenvalues in linear algebra.

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.

Eigenvalues and Eigenvectors of Markov Chains

Explores eigenvalues and eigenvectors of Markov chains, focusing on convergence rates and matrix properties.

Diagonalization of Symmetric Matrices

Covers the diagonalization of symmetric matrices and the spectral theorem.

Diagonalization of Symmetric Matrices

Explores diagonalization of symmetric matrices and their eigenvalues, emphasizing orthogonal properties.

Diagonalization in Symmetric Matrices

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

Matrix Similarity and Diagonalization

Explores matrix similarity, eigenvalues, and diagonalization in linear algebra.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, quadratic forms, diagonalization, and definiteness with examples and calculations.