Linear Systems: Stability and Solutions

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Related lectures (27)

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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.