Vector Spaces: Structure and Bases

Related lectures (26)

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Covers the basics of linear mapping and coordinate systems.

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Covers calculations in coordinates for vectors, including bases, scalar product, and determinants, with geometric interpretations and examples.

Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.

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

Covers matrices, linear applications, vector spaces, and bijective functions.

Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Covers determining vector spaces, calculating kernels and images, defining bases, and discussing subspaces and vector spaces.

Explains orthogonal families, bases, and projections in vector spaces.