Lectures related to Jordan Normal Form: Theory and Applications

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

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

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.

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

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

Explores the diagonalization of matrices and the conditions for exact diagonalization, with examples demonstrating the process.

Provides an overview of symmetric matrices, quadratic forms, and their applications in linear algebra and analysis.

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

Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.

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

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 symmetric matrices through orthogonal decomposition and the spectral theorem.

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

Covers the decomposition of matrices into triangular blocks and spectral decomposition.

Covers the concept of singular values in linear algebra and their properties, including diagonalization and practical examples.

Covers the basics of linear algebra, including matrix operations and singular value decomposition.