Jordan Form: Diagonalization and Nilpotent Matrices

Related lectures (24)

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

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

Introduces diagonalization by blocks and stable subspaces under linear transformations with examples and proofs.

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

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

Covers the Singular Value Decomposition theorem and its application in decomposing matrices.

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

Covers the concept of Singular Value Decomposition (SVD) for compressing information in matrices and images.

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