Basis (linear algebra)

Related lectures (23)

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Covers linear independence, bases of vectors, and solving systems using matrices.

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

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

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

Explores the properties of simple roots and reflections in Coxeter groups, emphasizing uniqueness and linear independence.

Explores the concept of linear independence in vector spaces through definitions and illustrative examples.

Explores linear combinations of vectors and matrices in Rn, demonstrating geometric interpretations and matrix operations.

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

Explores the Discrete Fourier Transform as a change of basis and the implications of having orthogonal vectors as a basis for complex numbers.

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.