Lectures related to Matrix Exponential: Properties and Applications

Diagonalization of Matrices

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

Diagonalization: Criteria and Examples

Covers the criteria for diagonalizing a matrix and provides illustrative examples.

Symmetric Matrices: Diagonalization

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Characteristic Polynomials and Similar Matrices

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

Jordan decomposition

Explores the unique decomposition of matrices into diagonalizable and nilpotent parts, showcasing their properties and applications.

Diagonalization: Eigenvectors and Eigenvalues

Covers the diagonalization of matrices using eigenvectors and eigenvalues.

Diagonalization of Matrices: Theory and Examples

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

Singular Value Decomposition: Applications and Interpretation

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

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.

Systems of n linear ODEs with constant coupling matrix A

Covers systems of n linear first-order ODEs with constant coupling matrix A and explores properties of solutions and the superposition principle.

Diagonalizable Matrices: Properties and Examples

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

Symmetric and Anti-symmetric Matrices

Introduces symmetric and anti-symmetric matrices, matrix powers, inverses, elementary matrices, and matrix manipulation.

Linear Algebra: Matrices and Operations

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

Linear applications and eigenvalues

Covers the representation of linear applications through matrices, diagonalizable matrices, bases, dot product, orthogonality, and orthogonal vectors.

Systems of Equations and Matrices

Covers systems of equations, matrices, solving examples, and consequences of invertible matrices.

Orthogonal Matrices & Spectral Decomposition

Covers the process of finding orthogonal bases and spectral decomposition of symmetric matrices.

Eigen Library for Linear Algebra

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

Linear Differential Equations

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

Linear Systems: Continuous Time

Covers linear systems in continuous time, stability analysis, and mass-spring system examples.