Linear Systems: Diagonal and Triangular Matrices, LU Factorization

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Page 2 of 3

Provides an overview of symmetric matrices, quadratic forms, and their applications in linear algebra and analysis.

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

Covers the Singular Value Decomposition theorem and its application in decomposing matrices.

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

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

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

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

Covers LU factorization, linear independence, and matrix equations.

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