Lectures related to Commuting matrices

Diagonalizable Matrices: Properties and Eigenvalues

Explores the properties of diagonalizable matrices and their eigenvalues for different parameters.

Covers the decomposition of linear operators and properties of eigenspaces.

Linear Algebra: Reduction of Linear Application

Covers the reduction of a linear application and finding corresponding reduced forms and bases.

Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.

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.

Diagonalizable Matrices: Properties and Examples

Explores the properties and examples of diagonalizable matrices, emphasizing the relationship between eigenvectors and eigenvalues.

Diagonalizable Matrices: Properties and Bases

Covers properties of diagonalizable matrices, invertibility, and basis of eigenspaces.

Diagonalizable Matrices

Covers the process of determining if a matrix is diagonalizable.

Diagonalizable Matrices: Properties and Determinants

Explains the properties and determinants of diagonalizable matrices in linear algebra.

Eigenvalues and Diagonalization

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

Orthogonal Matrices and Triangular Matrices

Explores properties of orthogonal and triangular matrices with linearly independent columns and their mathematical operations.

Spectral Decomposition

Explores spectral and singular value decompositions of matrices.

Direct Methods for Linear Systems

Covers the solution of linear systems using direct methods and the evolution of matrices.

Modern Regression: Smoothing and Modelling Choices

Explores roughness penalty, band matrices, and Bayesian inference in regression smoothing.

Finite Difference Methods: Linear Systems and Band Matrices

Covers the application of finite difference methods to solve partial differential equations.

Lie Algebras and Representations

Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.

Complex Numbers: Notations and Operations

Covers notations, operations, isomorphism, and polar decomposition of complex numbers.

Eigenspaces: Definitions and Examples

Introduces eigenspaces in linear algebra through definitions and practical examples of determining eigenspaces for matrices.

Rank of the Dual Map: Theorem 7.6

Explores Theorem 7.6 on the rank of the dual map in linear applications and delves into matrices and scalar matrices.

Linear Differential Equations

Covers the solution of linear differential equations, focusing on complex solutions and diagonalizable matrices.