Lectures related to Linear Systems: Continuous Time

Explores stability and solutions of linear systems in continuous and discrete time.

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

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

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

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

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.

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

Explores the properties of invertible matrices, including unique solutions and linear independence.

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

Covers the diagonalization of matrices using eigenvectors and eigenvalues.

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Covers linear systems, diagonal and triangular matrices, and LU factorization.

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

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

Explores properties of 3x3 matrices with real coefficients and determinant calculation methods.

Introduces key concepts in linear algebra, including matrices, operations, and numerical invariants.

Explores the diagonalization of symmetric matrices through orthogonal decomposition and the spectral theorem.

Covers matrix operations, focusing on the product and inverse of matrices.

Covers the Singular Value Decomposition (SVD) in detail, including properties of matrices and system linearity.

Explores diagonalization in 3D linear algebra, covering conditions for diagonalizability and eigenvectors.