Lectures related to Controllability of Linear Systems

Controllability and Observability

Covers controllability and observability in linear systems, discussing necessary conditions and implications of unimodular matrices.

Matrix Operations: Linear Systems and Solutions

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Singular Value Decomposition (SVD)

Covers the Singular Value Decomposition (SVD) in detail, including properties of matrices and system linearity.

Characteristic Polynomials and Similar Matrices

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

Linear Algebra: Change of Basis Matrices

Explores change of basis matrices in linear algebra, emphasizing the importance of understanding matrix transformations between different bases.

Linear Algebra: Basis and Matrices

Covers the concept of basis, linear transformations, matrices, inverses, determinants, and bijective transformations.

Eigen Library for Linear Algebra

Explores the Eigen library for linear algebra, covering vectors, matrices, arrays, memory management, reshaping, and per-component operations.

Singular Value Decomposition: Applications and Interpretation

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Linear Algebra: Applications and Matrices

Explores linear algebra concepts through examples and theorems, focusing on matrices and their operations.

Stability of ODE

Explores the stability of Ordinary Differential Equations, focusing on solution dependence, critical data, linearization, and control of nonlinear systems.

Characterization of Invertible Matrices

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

Linear Algebra in 3D: Determinants and Inverses

Explores determinants in 3D space and their role in linear algebra.

Linear Applications: Matrices and Transformations

Covers linear applications, matrices, transformations, and the principle of superposition.

Generalization of Change of Basis Matrices

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

Linear Algebra in 3D: Images and Kernels

Explores linear applications in 3D, emphasizing images, kernels, and solution uniqueness in systems.

Linear Algebra: Matrix Operations and Basis

Explores matrix operations, rank determination, kernel dimensions, and basis concepts in linear algebra.

Matrix Representations of Linear Applications

Covers the matrix representations of linear applications and the equivalence between matrices.

Vector Spaces: Properties and Operations

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Linear Algebra: Multilinear Groin and Determinants

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

Diagonalization of Matrices: Theory and Examples

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.