Linear Algebra: Singular Value Decomposition

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Related lectures (25)

Explores subspaces, spectra, and projections in linear algebra, including symmetric matrices and orthogonal projections.

Spectral Decomposition

Explores spectral and singular value decompositions of matrices.

Singular Value Decomposition: Applications and Interpretation

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Linear Algebra Review

Covers the basics of linear algebra, including matrix operations and singular value decomposition.

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.

Eigenvalues and Eigenvectors Decomposition

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

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.

Characteristic Polynomials and Similar Matrices

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

Diagonalization of Symmetric Matrices

Explores the diagonalization of symmetric matrices through orthogonal decomposition and the spectral theorem.

Decomposition Spectral: Symmetric Matrices

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Matrix Diagonalization: Spectral Theorem

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

Canonical Correlation Analysis: Overview

Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.

SVD: Singular Value Decomposition

Covers the concept of Singular Value Decomposition (SVD) for compressing information in matrices and images.

Linear Regression: Absence or Presence of Covariates

Explores linear regression with and without covariates, covering models captured by independent distributions and tools like subspaces and orthogonal projections.

Matrix Decomposition: Triangular and Spectral

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

Diagonalization of Symmetric Matrices

Explores the diagonalization of symmetric matrices and the importance of Singular Value Decomposition.

Symmetric Matrices: Properties and Decomposition

Covers examples of symmetric matrices and their properties, including eigenvectors and eigenvalues.

Linear Regression Testing

Explores least squares in linear regression, hypothesis testing, outliers, and model assumptions.

Singular Value Decomposition

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

Orthogonal Bases and Projection

Introduces orthogonal bases, projection onto subspaces, and the Gram-Schmidt process in linear algebra.

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