Linear Systems: LU Factorization with Pivoting

Related lectures (28)

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Covers the LU decomposition algorithm, transforming a matrix into L and U.

Explores matrix inversion, conditions for invertibility, uniqueness of the inverse, and elementary matrices for inversion.

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

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

Covers the resolution of linear systems and its link to optimization problems.

Explores operations with triangular matrices and their role in solving linear systems.

Introduces the Gauss elimination algorithm for solving linear systems with practical examples in Python.

Explores LU decomposition for solving linear systems, focusing on determinants and cofactors.

Covers the formulation of linear systems, direct and iterative methods for solving them, and the cost of LU factorization.

Explores the link between linear systems and optimization through elimination and LU decomposition.