Base Changes and Rank

Related lectures (29)

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Covers kernels and images of linear transformations between vector spaces, illustrating properties and providing proofs.

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

Explains how to calculate the dimension of a kernel of a matrix transpose.

Explores linear applications in 3D, emphasizing images, kernels, and solution uniqueness in systems.

Covers the concept of basis, linear transformations, matrices, inverses, determinants, and bijective transformations.

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

Explores linear applications, vector spaces, kernels, and invertibility in linear algebra.

Covers the concepts of kernel and image of a linear application in linear algebra.

Explores the associated matrix of a linear map, basis formation, and space relationships.

Delves into the Rank Theorem's implications for linear transformations and mappings.