Linear Algebra: Matrix Decomposition and Base Change

Related lectures (23)

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

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

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

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.

Covers linear applications, matrices, transformations, and the principle of superposition.

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

Covers the reduction of a linear application and finding corresponding reduced forms and bases.

Covers the Singular Value Decomposition (SVD) of a matrix and its applications.

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

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