Singular Value Decomposition

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Matrices and Quadratic Forms: Key Concepts in Linear Algebra

Provides an overview of symmetric matrices, quadratic forms, and their applications in linear algebra and analysis.

Factorisation QR: Gram-Schmidt Process

Covers the Factorisation QR theorem and the Gram-Schmidt method for orthonormal bases.

QR Factorization: Least Squares System Resolution

Covers the QR factorization method applied to solving a system of linear equations in the least squares sense.

Singular Value Decomposition: Example

Explains the step-by-step process of finding the singular value decomposition of a matrix.

Singular Value Decomposition: Fundamentals and Applications

Explores the fundamentals of Singular Value Decomposition, including orthonormal bases and practical applications.

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.

Jordan decomposition

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

Characteristic Polynomials and Similar Matrices

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

Linear Algebra: Matrix Decomposition and Base Change

Covers the algorithm for matrix decomposition and base change in linear algebra.

Singular Value Decomposition

Covers the Singular Value Decomposition theorem and its application in decomposing matrices.