Advanced analysis II

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Related lectures (31)

Page 1 of 4

Stationary Points and Saddle Points

Explores stationary points, saddle points, symmetric matrices, and orthogonal properties in optimization.

Matrix Diagonalization: Spectral Theorem

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

Symmetric Matrices: Diagonalization

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

Symmetric Matrices: Eigenvalues and Eigenvectors

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

Characteristic Polynomials and Similar Matrices

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

Implicit Function Theorem

Explores the Implicit Function Theorem, supporting hyperplanes, local extrema, and higher-order derivatives, concluding with the classification of stationary points.

Calcul de valeurs propres

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

Diagonalization of Matrices

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

Eigenvalues and Eigenvectors Decomposition

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

Non-Negative Definite Matrices and Covariance Matrices

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