Lectures related to Linear Systems: Stability and Solutions

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

Singular Value Decomposition: Applications and Interpretation

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

Diagonalization of Linear Transformations

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

Diagonalization of Matrices: Theory and Examples

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

Diagonalizable Matrices: Properties and Examples

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

Matrix Similarity and Diagonalization

Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.

Linear Systems: Diagonal and Triangular Matrices, LU Factorization

Covers linear systems, diagonal and triangular matrices, and LU factorization.

Diagonalization of Matrices

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

Diagonalization: Eigenvectors and Eigenvalues

Covers the diagonalization of matrices using eigenvectors and eigenvalues.

Network Functions: Analysis and Design

Explores network functions in s-domain circuit analysis, covering stability, poles, responses, and design.

Diagonalization of Matrices

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

Jordan decomposition

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

Signals & Systems I: Characteristic Modes and Impulse Responses

Explores characteristic modes, impulse responses, and system stability in signals and systems.

The Frequency Response of RLC Circuits

Explores the frequency response of RLC circuits, operational amplifiers, and linear dependent sources, highlighting the historical significance of operational amplifiers.

System Identification and Stability

Explores system identification, stability criteria, and challenges in stabilizing cameras on moving platforms.

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.

Characterization of Invertible Matrices

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

Diagonalization Cream: Distinct Eigenvalues

Covers the diagonalization of matrices with distinct eigenvalues and the importance of this process.

Diagonalisation: Theorem and Demonstration

Explores diagonalization conditions, bases by eigenvectors, and generalization of concepts.