QR Factorization and Least Squares

Related lectures (27)

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

Introduces the Gram-Schmidt algorithm, QR factorization, and the method of least squares.

Explores Gram-Schmidt process, orthogonal projection, QR factorization, and least squares solutions for linear systems.

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

Explains the concept of least squares solutions and their application in finding the closest solution to a system of equations.

Explains Singular Value Decomposition, focusing on orthogonal vectors and matrix decomposition.

Explains the QR factorization theorem and demonstrates the Gram-Schmidt procedure with an example.

Explores matrix equivalence theorems for systems of equations and least squares solutions.

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

Covers the QR factorization of a matrix A into Q and R.