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Lecture
Singular Values: Definitions and Properties
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Related lectures (24)
Characteristic Polynomials and Similar Matrices
Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.
Eigenvalues and Eigenvectors Decomposition
Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.
Singular Value Decomposition: Applications and Interpretation
Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.
Diagonalization of Linear Transformations
Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.
Matrix Diagonalization: Spectral Theorem
Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.
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.
Diagonalization of Linear Transformations
Covers the diagonalization of linear transformations in R^3, exploring properties and examples.
Singular Value Decomposition
Covers the Singular Value Decomposition theorem and its application in decomposing matrices.
Singular Value Decomposition (SVD)
Covers the Singular Value Decomposition (SVD) in detail, including properties of matrices and system linearity.
Diagonalization of Matrices: Theory and Examples
Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.
Linear Algebra Review: Convex Optimization
Covers essential linear algebra concepts for convex optimization, including vector norms, eigenvalue decomposition, and matrix properties.
Canonical Correlation Analysis: Overview
Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.
Diagonalization of Symmetric Matrices
Explores the diagonalization of symmetric matrices through orthogonal decomposition and the spectral theorem.
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.
SVD: Singular Value Decomposition
Covers the concept of Singular Value Decomposition (SVD) for compressing information in matrices and images.
Linear Algebra Basics
Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.
Diagonalization of Matrices
Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.
Eigenvalues and Eigenvectors in 3D
Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.
Linear Algebra Review
Covers the basics of linear algebra, including matrix operations and singular value decomposition.
Diagonalization of Matrices
Explains the diagonalization of matrices, criteria, and significance of distinct eigenvalues.
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