Lectures related to Determinants: Theory and Applications

Determinants: Alternate Forms and Symmetrization

Explores alternate forms, symmetric forms, and determinants in linear algebra.

Linear Algebra: Multilinear Groin and Determinants

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

Determinants: Properties and Applications

Explores the properties and applications of determinants in linear algebra.

Linear Algebra: Multilinear Forms

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

Linear Algebra in 3D: Determinants and Inverses

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

Linear Algebra: Multilinear Forms

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

Linear Algebra in 3D: Matrices and Determinants

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

Linear Algebra: Systems of Equations

Explores solving systems of equations using matrices and determinants.

Tensor Products of Modules

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

Linear Algebra: Multilinear Forms

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

Operations on Linear Applications

Covers operations on linear applications in R³, including definitions, behavior of compositions, and determinants.

Matrix Calculus: Rank and Decomposition

Covers matrix rank, determinant, and decomposition in linear algebra.

Algebraic Varieties in Linear Algebra

Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.

Linear Algebra: Matrices and Operations

Covers the basics of linear algebra, focusing on matrices and operations.

Determinants of Matrices: Properties and Applications

Explores the properties and applications of determinants of matrices in linear algebra.

Linear Algebra: Basis and Matrices

Covers the concept of basis, linear transformations, matrices, inverses, determinants, and bijective transformations.

Bilinear Forms: Theory and Applications

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

Tensor Products and Symmetric Power

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

Linear Transformations in R³

Covers operations on linear applications in R³, including composition, addition, and determinants.

Linear Algebra: Rank Theorem

Explores the Rank Theorem in linear algebra, covering matrix properties and determinants.