Linear Algebra: Bases and Transformations

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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.

Linear Algebra Basics

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Diagonalization of Linear Transformations

Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.

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 Matrices and Least Squares

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

Linear Applications Overview

Explores linear applications, vector spaces, kernels, and invertibility in linear algebra.

Eigenvalues: Finding Methods

Explains methods for finding eigenvalues in linear algebra through examples.

Singular Value Decomposition (SVD)

Covers the Singular Value Decomposition (SVD) in detail, including properties of matrices and system linearity.

Singular Values: Definitions and Properties

Covers the concept of singular values in linear algebra and their properties, including diagonalization and practical examples.

Linear Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.