Lectures related to Algebraic Varieties in Linear Algebra

Linear Transformations: Matrices and Applications

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

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

Dimension of Algebraic Variety

Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.

Linear Algebra: Matrix Operations

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

Algebraic Varieties: Projective Sets and Topology

Explores projective algebraic sets, prime ideals, irreducible sets, cones, and Nullstellensatz theorem.

Matrix Calculus: Rank and Decomposition

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

Linear Applications: Vectorial Structure

Explores the vectorial structure of linear applications, including addition, scalar multiplication, and matrix representation.

Linear Algebra: Multilinear Groin and Determinants

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