Linear Transformations: Matrices and Bases

Related lectures (26)

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Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Explores polynomial operations, properties, and subspaces in vector spaces.

Covers the determination of matrices associated with linear transformations and explores the kernel and image concepts.

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

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

Explores linear independence, bases, and dimension in vector spaces with examples involving matrices and polynomials.

Introduces linear algebra basics, including linear independence, injectivity, surjectivity, and bases in vector spaces.