Linear Algebra: Basis and Canonical Basis

Related lectures (22)

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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.