Lectures related to Minimal polynomial (linear algebra)

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

Explains how to find free variables in matrix equations and analyze characteristic polynomials.

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

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

Covers the diagonalization of matrices with distinct eigenvalues and the importance of this process.

Covers the decomposition of linear operators and properties of eigenspaces.

Covers the reduction of a linear application and finding corresponding reduced forms and bases.

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

Explores minimal annihilating polynomials and cyclic invariant subspaces, showcasing their practical applications through matrix computations.

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

Explores eigenvalues and minimal polynomial, emphasizing their importance in linear algebra.

Covers the solutions of homogeneous linear differential equations and how to find linearly independent solutions.

Covers the theory and applications of orthogonal projections, focusing on the Gram-Schmidt process for orthonormalization.

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

Covers the concept of polynomial characteristic of a matrix and its relation to eigenvalues.

Explores characteristic polynomials, eigenvalues, and eigenvectors of matrices A, B, C, D, and E.

Explores diagonalizing matrices, similarity, eigenvectors, and proper spaces.

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

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

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