Linear Transformations and Basis Changes

Related lectures (24)

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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 vector subspaces in R4, symmetric matrices, basis vectors, and canonical forms.

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

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

Covers elementary matrix operations and vector spaces, including properties and conditions for invertibility.

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

Explains linear independence, basis, and matrix rank with examples and exercises.

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