Lectures related to Permutation matrix

Matrix Operations: Inverse and Reduction to Echelon Form

Covers matrix operations and reduction to echelon form with practical examples.

Linear Systems: LU Factorization with Pivoting

Explains the Gaussian elimination algorithm with pivoting and LU factorization for linear systems.

Counting: Permutations and Combinations

Covers permutation, combination, and the pigeonhole principle in counting problems.

Consensus in Networked Control Systems

Explores consensus in networked control systems through graph weight design and matrix properties.

Elementary Matrices

Covers elementary matrices and their operations in matrix algebra, highlighting their importance in linear algebra.

Determinants: Special Linear Groups and Matrix Properties

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

Steinitz Lemma and Cycles

Explores the Steinitz Lemma and the concept of cycles in linear algebra.

Matrix Inversion

Explores matrix inversion, conditions for invertibility, uniqueness of the inverse, and elementary matrices for inversion.

Consensus in Networked Control Systems

Explores consensus in networked control systems, covering convergence properties, normalization of eigenvectors, and rate of convergence.

Floating Point Numbers: LU Decomposition and Errors

Explores floating point numbers, LU decomposition, errors, and matrix properties.

Orthogonality and Least Squares Method

Explains matrix operations, orthogonality, and least squares method in solving linear equations.

Linear Equations and Matrices: Solution Methods, Elementary Operations

Explores solution methods and elementary operations for linear equations and matrices, demonstrating techniques to simplify systems and obtain solutions.

Local structure of totally disconnected locally compact groups I

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

LU Factorization Criteria

Explores the conditions for LU factorization without permutation and diagonal dominance in matrices.

Consensus Theorem for Communication Networks

Explores the consensus theorem for communication networks and the implications of various consensus properties in networked control systems.

Discrete Dynamical Systems

Explores eigenvalues, determinants, traces, and stochastic matrices in discrete dynamical systems.

Symmetric Group and Group Actions

Covers the Symmetric group, cycle decomposition, transpositions, even and odd permutations, and group actions.

Linear Maps: Basis and Applications

Explores linear maps, basis freedom, composition, coordinates in different bases, associated matrices, and coefficients.

Counting: Combinations and Permutations

Covers the concepts of combinations and permutations in counting scenarios.

Solving Linear Systems: Methods and Solutions

Explores methods for solving linear systems and building solutions step by step.