Linear Algebra: Basis and Canonical Basis

Related lectures (22)

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Covers vector spaces, operations, and linear independence with examples from polynomials and functions.

Covers the definition and use of coordinate systems and applications in bases and linear equations.

Explores vector spaces, linear independence, and spanning sets in linear algebra.

Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.

Covers linear independence, bases, change of basis, and vector representation.

Covers vector spaces, subspaces, kernel, image, linear independence, and bases in linear algebra.

Explores linear dependence theorems and proofs, emphasizing the importance of understanding linear dependence in linear algebra.

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.