Gram-Schmidt Algorithm: Orthogonalization and QR Factorization

Related lectures (24)

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

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

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

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

Explains linear independence, basis, and matrix rank with examples and exercises.

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

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

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

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

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