Lectures related to Determinants: Properties and Applications

Linear Algebra: Multilinear Groin and Determinants

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

Determinants: Theory and Applications

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

Linear Algebra in 3D: Determinants and Inverses

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

Determinants: Alternate Forms and Symmetrization

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

Cramer's Rule and Volume

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

Change of Basis, Passage Matrices

Explores change of basis and passage matrices in linear algebra, with a focus on properties and practical examples.

Spherical Coordinates: Determinant of Jacobi

Covers spherical coordinates and the determinant of Jacobi in linear algebra.

Linear Algebra Basics

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Characteristic Polynomials and Similar Matrices

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

Linear Algebra in 3D: Matrices and Determinants

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

Linear Algebra: Rank Theorem

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

Operations on Linear Applications

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

Invertible Matrices: Definitions and Properties

Explores the definitions and properties of invertible matrices, including determinants and uniqueness of solutions.

Determinants of Matrices: Properties and Applications

Explores the properties and applications of determinants of matrices 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: Matrix Operations and Basis

Explores matrix operations, rank determination, kernel dimensions, and basis concepts in linear algebra.

Linear Algebra: Basis and Matrices

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

Linear Algebra: Cramer's Rule

Covers Cramer's Rule for solving linear equations using determinants.

Linear Algebra: Systems of Equations

Explores solving systems of equations using matrices and determinants.

Linear Algebra: Determinants and Applications

Explores determinants, similarity invariance, Cramer's formula, and geometric interpretations in matrices.