Linear Dynamical Systems Lecture 15-Inputs and Outputs of symmetric matrices

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Linear Dynamical Systems Lecture 14- Applications of Jordan Canonical Form in LDS and Electrical Engineering

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Linear Dynamical Systems Lecture 13-generalized eigenvectors, diagonalization, and Jordan canonical form

Jordan normal form (often called Jordan canonical form) shows that a given square matrix M over a field K containing the eigenvalues of M can be transformed into a certain normal form by changing the basis. This normal form is almost diagonal in the sense that its only non-zero entries lie on the diagonal and the superdiagonal. This is made more precise in the Jordan-Chevalley decomposition. One can compare this result with the spectral theorem for normal matrices, which is a special case of the Jordan normal form.

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Linear Dynamical Systems Lecture 3-Linear algebra

Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear maps (also called linear transformations), and systems of linear equations. Vector spaces are a central theme in modern mathematics; thus, linear algebra is widely used in both abstract algebra and functional analysis. Linear algebra also has a concrete representation in analytic geometry and it is generalized in operator theory. It has extensive applications in the natural sciences and the social sciences, since nonlinear models can often be approximated by linear ones.

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