Matrix Factorization: LU Decomposition

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Introduces LU decomposition for efficient linear equation solving using matrix factorization.

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

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

Covers the LU decomposition method applied to linear systems, presenting the system in two steps.

Covers direct methods for solving linear systems in numerical analysis.

Explains the Gaussian elimination algorithm with pivoting and LU factorization for linear systems.

Covers the basics of linear algebra, including matrix operations and singular value decomposition.

Explores the Cholesky factorization method for symmetric positive definite matrices.

Explores direct methods for solving linear systems of equations, including Gauss elimination and LU decomposition.

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