Lectures related to Linear algebraic groups

Linear Algebra: Matrix Operations

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

Dynamics on Homogeneous Spaces and Interactions with Number Theory

Explores dynamics on homogeneous spaces and their interactions with number theory, focusing on modular lattices and the Iwasawa decomposition theorem.

Determinants: Special Linear Groups and Matrix Properties

Explores the special linear group, matrix properties, and determinant theorems.

Characteristic Polynomials and Similar Matrices

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

The Torus and Linear Groups

Explores the torus, linear groups, stability properties of matrices, and homomorphisms.

Characterization of Invertible Matrices

Explores the properties of invertible matrices, including unique solutions and linear independence.

Linear Systems: Diagonal and Triangular Matrices, LU Factorization

Covers linear systems, diagonal and triangular matrices, and LU factorization.

Matrix Operations: Product and Inverse

Covers matrix operations, focusing on the product and inverse of matrices.

Linear Algebra: Matrices Properties

Explores properties of 3x3 matrices with real coefficients and determinant calculation methods.

Linear Algebra: Matrices and Inverses

Explores matrices, inverses, and their applications in linear algebra, emphasizing composition and transformation properties.

Diagonalization of Matrices

Explains the diagonalization of matrices, criteria, and significance of distinct eigenvalues.

Linear Algebra Basics

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

Matrix Operations: Scaling and Invertibility

Covers scaled matrices, ladder matrices, and the Gauss method for matrix operations.

Diagonalization of Linear Transformations

Covers the diagonalization of linear transformations in R^3, exploring properties and examples.

Characters: Linear Algebraic Groups

Introduces characters as group homomorphisms from linear algebraic groups to multiplicative groups.

Linear Applications and Matrix Calculus

Explores linear applications, matrices, injectivity, unique solutions, and matrix operations.

Matrix Decomposition: Triangular and Spectral

Covers the decomposition of matrices into triangular blocks and spectral decomposition.

Triangular Block Matrices

Explores upper triangular block matrices, invertibility, elementary transformations, and determinants with examples.

Linear Algebra: Matrices and Operations

Introduces key concepts in linear algebra, including matrices, operations, and numerical invariants.

Eigenvalues and Diagonalization

Explores eigenvalues, diagonalization, and matrix similarity, showcasing their importance and applications.