Singular Value Decomposition: Theory and Applications

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Explores spectral and singular value decompositions of matrices.

Covers the construction of an iterative method for linear systems, emphasizing matrix decomposition and convexity.

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

Explains the method of least squares in linear regression to find the best-fitting line to a set of data points.

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

Covers phase portraits, eigenvalue decomposition, Jordan decomposition, and stable nodes in non-linear systems.

Explores QR factorization and the least squares method for solving systems of equations.

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

Explores the Cholesky factorization method for symmetric positive definite matrices.

Covers the construction of an iterative method for linear systems by decomposing a matrix A into P, T, and P_A.