Linear Algebra: Change of Basis

Related lectures (21)

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

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

Explores vector spaces in three dimensions, covering linear combinations, subspaces, and properties of families of vectors in R³.

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

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

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

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

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

Covers the method to calculate the images of vectors in a given base.

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