Matrix Calculus: Rank and Decomposition

Related lectures (27)

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Covers vector spaces, bases, and decomposition of vectors in R³.

Covers the matrix representations of linear applications and the equivalence between matrices.

Introduces key concepts in linear algebra, including matrices, operations, and numerical invariants.

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

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.

Covers the norm of a matrix, operator, singular values, and unitary matrices in linear algebra.

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

Covers the matrix representations of linear applications and how to find representative matrices.

Covers the properties and calculations of matrix determinants, including special cases and examples.