Pseudo Jordan canonical form

Mancini, Manuel
(2023) JCTS: Junior Category Theory Seminar — Location: Louvain-la-Neuve, Belgium (6.May.2023)

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(en) In this talk we introduce the Pseudo Jordan Canonical Form, also known as Real Jordan Canonical Form, which is an analogous of the Jordan normal form over the field of real numbers. Then we use this to show a generalized version of the Spectral Theorem for real normal matrices i.e., real matrices A such that AA*=A*A, where A* denotes the transpose matrix of A. These results have some applications in Lie Groups theory. For instance, one can prove that the unitary group U(n) and the special unitary group SU(n) are both connected Lie groups.
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Mancini, M. (2023, May). Pseudo Jordan canonical form. JCTS: Junior Category Theory Seminar, Louvain-la-Neuve, Belgium. https://hdl.handle.net/2078.5/279080