Numerical Analysis: Direct Methods for Linear Systems

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Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.

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

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

Explores LU decomposition of a matrix into lower and upper triangular matrices.

Explains Gaussian elimination and LU factorization for solving linear systems of equations.

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

Covers LU factorization, linear independence, and matrix equations.

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

Covers the analysis of linear systems, focusing on methods such as Jacobi and Richardson for solving linear equations.