Linear Systems: Direct Methods

Related lectures (31)

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

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

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

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

Covers LU factorization, linear independence, and matrix equations.

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

Covers the analysis of the column space of a matrix and its implications.

Covers methods to solve linear systems with a finite number of operations.

Covers the construction of an iterative method for linear systems by decomposing a matrix A into P, T, and P_A.

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