Linear Algebra Review

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Related lectures (26)

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Matrix Decomposition: Triangular and Spectral

Covers the decomposition of matrices into triangular blocks and spectral decomposition.

Matrix Inversion

Explores matrix inversion, conditions for invertibility, uniqueness of the inverse, and elementary matrices for inversion.

Characteristic Polynomials and Similar Matrices

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

Singular Value Decomposition: Orthogonal Vectors and Matrix Decomposition

Explains Singular Value Decomposition, focusing on orthogonal vectors and matrix decomposition.

Singular Value Decomposition

Introduces Singular Value Decomposition (SVD) in linear algebra, covering matrix factorization and properties with practical examples.

Eigenvalues and Eigenvectors Decomposition

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

Linear Algebra: Matrices Properties

Explores properties of 3x3 matrices with real coefficients and determinant calculation methods.

Convex Optimization: Linear Algebra Review

Provides a review of linear algebra concepts crucial for convex optimization, covering topics such as vector norms, eigenvalues, and positive semidefinite matrices.

Singular Value Decomposition

Explores Singular Value Decomposition, low-rank approximation, fundamental subspaces, and matrix norms.

Jordan decomposition

Explores the unique decomposition of matrices into diagonalizable and nilpotent parts, showcasing their properties and applications.