Lectures related to Networked Control Systems: Consensus and Connectivity

Spectral Properties of Non-negative Matrices

Covers the spectral properties of non-negative matrices and their interpretation in digraphs.

Numerical Analysis: Linear Systems

Covers the analysis of linear systems, focusing on methods such as Jacobi and Richardson for solving linear equations.

Primitive Matrices and Spectral Properties in Networked Control Systems

Explores primitive matrices, dominant eigenvalues, and spectral properties in networked control systems.

Characteristic Polynomials and Similar Matrices

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

Diagonalization of Linear Transformations

Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.

Eigenvalues and Fibonacci Sequence

Covers eigenvalues, eigenvectors, and the Fibonacci sequence, exploring their mathematical properties and practical applications.

Matrix Equations: Finding Free Variables

Explains how to find free variables in matrix equations and analyze characteristic polynomials.

Diagonalization Method: Application and Properties

Covers the method of diagonalization for determining if a non-square matrix A is diagonalizable.

Irreducible Matrices and Strong Connectivity

Explores irreducible matrices and strong connectivity in networked control systems, emphasizing the importance of adjacency matrices and graph structures.

Diagonalization of Linear Transformations

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

Diagonalization of Symmetric Matrices

Explores the diagonalization of symmetric matrices through orthogonal decomposition and the spectral theorem.

State-Space Representation: Controllability and Observability

Explores state-space representation, controllability, observability, and regulator calculation using the Ackermann method.

Determinant of a Matrix

Covers the properties and calculations of the determinant of a matrix.

State-Space Representation: Structure Theorem

Covers the structure theorem for state-space representations and companion forms.

Orthogonally Diagonalizable Matrices

Explores orthogonally diagonalizable matrices, eigenvectors, bases, and matrix properties.

Eigenvalues and Similar Matrices

Explores eigenvalues, matrix trace, and similarity, highlighting their significance in matrix properties.

Linear Algebra: Matrix Representation

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.

Linear Algebra: Matrices and Linear Applications

Covers matrices, linear applications, vector spaces, and bijective functions.

Diagonalization of Symmetric Matrices

Explores diagonalization of symmetric matrices and their eigenvalues, emphasizing orthogonal properties.

Eigenvalues and Diagonalization

Explores eigenvalues, eigenvectors, and matrix diagonalization with examples and proofs.