Lectures related to Linear Algebra: Basis and Canonical Basis

Explains linear independence, basis, and matrix rank with examples and exercises.

Explores vector spaces, subspaces, bases, and linear combinations in R² and R³, including free and linked families.

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

Covers linear independence, bases, and coordinate systems with examples and theorems.

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Explores linear independence in vector spaces and the concept of bases.

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Covers the basics of linear mapping and coordinate systems.

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

Explores linear combinations, basis determination, and vector space dimensionality through practical examples and exercises.

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.