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Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Explores the properties of invertible matrices, including unique solutions and linear independence.

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

Explores diagonalization in 3D linear algebra, covering conditions for diagonalizability and eigenvectors.

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

Explores matrix representations of linear maps and their invariance, using examples and special cases.

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

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.

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

Explores properties of 3x3 matrices with real coefficients and determinant calculation methods.

Covers matrix transposition, rank, and basis change in linear algebra, exploring invertibility criteria and basis relationships.

Covers the process of finding a base from a system of generators in linear algebra.

Covers the matrix representation of a linear transformation and its properties, including bases and coefficients.

Covers the basics of linear mapping and coordinate systems.

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

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

Covers the concept of lines spaces and equivalent matrices in linear algebra.

Explores linear algebra concepts through examples and theorems, focusing on matrices and their operations.

Covers linear applications, matrices, transformations, and the principle of superposition.

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