Polynomial Characteristic: Definition, Properties, and Applications

Related lectures (30)

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

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

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

Covers eigenvalues and eigenvectors, explaining their importance in linear algebra.

Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.

Explains the step-by-step process of finding the singular value decomposition of a matrix.

Covers bases, transformations, and matrix decompositions in linear algebra.

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

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

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