Factorisation LU

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Covers direct methods for solving linear systems in numerical analysis.

Covers linear systems, diagonal and triangular matrices, and LU factorization.

Covers LU factorization, linear independence, and matrix equations.

Explores the properties of invertible matrices, including unique solutions and linear independence.

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

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

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

Covers LU factorization, determinants, subspaces, and matrix products.

Explores LU decomposition for matrix factorization and solving linear systems.

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