Concept

Jordan matrix

Related lectures (30)

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Matrix Exponential and Jordan Normal Form

Covers the matrix exponential, its convergence properties, and the Jordan normal form.

Jordan Normal Form

Covers the Jordan Normal Form and the identification of torsion blocks within matrices.

Jordan Normal Form: Part 1

Covers the Jordan normal form and the decomposition of vector spaces by an endomorphism.

Exponential of Operators and Matrices

Covers the exponential of operators and matrices, commutation properties, Jordan normal form, and linear algebra concepts related to linear operators and eigenvalue problems.

Diagonalization of Matrices: Eigenvectors and Eigenvalues

Covers the concept of diagonalization of matrices through the study of eigenvectors and eigenvalues.

Jordan Normal Form

Covers the Jordan Normal Form theorem and invariance of kernels under transformations.

Diagonalization of Linear Maps

Explores the diagonalization of linear maps by finding a basis formed by eigenvectors.

Non-Diagonalizable Case: Simple Eigenvalue (Theory)

Explores the reduction of a linear transformation with a single real eigenvalue.

Jordan Normal Form: Theory and Applications

Explores the Jordan normal form and its applications in linear algebra, focusing on diagonalization and cyclic bases.

Jordan Normal Form

Covers the Jordan Normal Form and its application in linear algebra.

Linear Systems: Equilibria and Stability

Explores linear systems' equilibria, stability, and modes, including Lyapunov stability and exponential stability.

Modes and Stability of LTI Systems

Explores the analysis of free states and modes in multivariable control systems, emphasizing stability properties and practical examples.

Linear Algebra: Cofactors and Eigenvectors

Explains cofactors, eigenvectors, eigenvalues, and studying linear applications.

Algebraic Multiplicity, Geometric Multiplicity

Explores algebraic and geometric multiplicities of eigenvalues in linear algebra.

Jordan Form: Diagonalization and Nilpotent Matrices

Covers Jordan form, diagonalization, and nilpotent matrices, discussing properties and decomposition.

Jordan Form: Decomposition and Properties

Covers the decomposition of a matrix into Jordan blocks and the process of finding the Jordan form.

Diagonalization of Matrices

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

Diagonalizability Criterion

Covers the criterion for diagonalizability of matrices, focusing on comparing examples and understanding the relationship between algebraic and geometric multiplicities of eigenvalues.

Diagonalization: Step by Step

Explains the step-by-step process of diagonalization for linear transformations on finite-dimensional vector spaces.