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Explores linear applications in 3D, emphasizing images, kernels, and solution uniqueness in systems.

Covers bases, linear dependencies, injective and surjective transformations, and matrix representation in linear algebra.

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

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

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

Covers singular vectors in Liouville CFT, focusing on representation theory and their implications in mathematical physics.

Covers the theory and applications of bilinear forms in various mathematical contexts.

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

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

Explores linear models, least squares, Gaussian vectors, and model selection methods.

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

Explores the matrix representation of linear applications through examples and properties.

Explores the relationship between matrices under different bases in linear algebra.

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

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

Explores linear algebra basics, emphasizing matrix representations of transformations and the importance of choosing appropriate bases.