Linear Mapping and Bases

Related lectures (26)

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Covers the basics of linear mapping and coordinate systems.

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

Covers the reduction of a linear application and finding corresponding reduced forms and bases.

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

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

Explains kernel, image, and linear maps, illustrating concepts with examples.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Covers the extraction of bases from families of vectors and the concept of coordinate application in vector spaces.

Introduces orthogonal families, orthonormal bases, and projections in linear algebra.

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