Lectures related to Determinants: Alternate Forms and Symmetrization

Explores multilinear groin and determinants, including the Sarrus rule and proof by induction.

Covers the theory of determinants and their applications in linear algebra.

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

Covers the definition and properties of multilinear forms, emphasizing linearity and applications in mathematics.

Covers alternating and symmetric multilinear forms in vector spaces over a field.

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Explores the properties and applications of determinants in linear algebra.

Explores multilinear forms in linear algebra, emphasizing their role in vector space transformations.

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Explores multilinear forms in linear algebra, emphasizing their properties and applications.

Covers linear algebra in three dimensions, focusing on matrices and determinants.

Explores multilinear forms in linear algebra, emphasizing their properties and applications.

Covers fundamental linear algebra concepts like vector spaces and eigenvalues.

Explores determinants in 3D space and their role in linear algebra.

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

Explores permutations, signature, and alternating multilinear forms in vectors.

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Explores solving systems of equations using matrices and determinants.

Covers Cramer's Rule, matrix inverse, determinants, and volume in linear algebra.

Covers the Tucker decomposition and its applications in data compression, explaining the notion of multilinear rank and the HOSVD method.