Linear Algebra: Canonical Basis and Eigenvalues

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Explores vector space operations, linear transformations, matrix representation, and linear applications.

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

Covers the basics of linear mapping and coordinate systems.

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

Explains the diagonalization of matrices, criteria, and significance of distinct eigenvalues.

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

Covers the concept of diagonalization of matrices through the study of eigenvectors and eigenvalues.

Explores eigenvalues and eigenvectors, demonstrating their importance in linear algebra and their application in solving systems of equations.

Explores minimal annihilating polynomials and cyclic invariant subspaces, showcasing their practical applications through matrix computations.

Explains how to find free variables in matrix equations and analyze characteristic polynomials.