Cut-off Phenomenon

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Related lectures (30)

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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.

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.

Matrix Diagonalization: Spectral Theorem

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

Singular Values, Fundamental Theorem

Explores the fundamental theorem on singular values and the formation of orthonormal bases from eigenvectors.

Convergence of Random Walks

Explores the convergence of random walks on graphs and the properties of weighted adjacency matrices.

Eigenvalues and Eigenvectors Decomposition

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

Symmetric Matrices: Eigenvalues and Eigenvectors

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

Calcul de valeurs propres

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

Eigenvalues and Eigenvectors: Understanding Matrices

Explores eigenvalues and eigenvectors in matrices through examples and calculations.