Numerical Analysis: Direct Methods for Linear Systems

Related lectures (27)

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

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

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

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

Covers matrix operations, focusing on the product and inverse of matrices.

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

Explores properties of 3x3 matrices with real coefficients and determinant calculation methods.

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

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

Explores the Cholesky factorization method for symmetric positive definite matrices.