Linear Transformations: Isomorphism and Dimension

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Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Covers the concepts of kernel and image of a linear transformation and their relationship with the rank of the matrix.

Covers various examples and general concepts related to linear applications in algebra.

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

Explores changing bases in vector spaces and matrix representation of linear transformations.

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

Covers the basics of linear algebra, including linear maps, bases, and matrix operations.

Explains kernel, image, and linear maps, illustrating concepts with examples.

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