Unitary Diagonalization and Quadratic Forms

  • James B. CarrellEmail author


As we saw in Chap.  8, when V is a finite-dimensional vector space over \({\mathbb {F}}\), then a linear mapping \(T:V\rightarrow V\) is semisimple if and only if its eigenvalues lie in \({\mathbb {F}}\) and its minimal polynomial has only simple roots. It would be useful to have a result that would allow one to predict that T is semisimple on the basis of a criterion that is simpler than finding the minimal polynomial, which, after all, requires knowing the roots of the characteristic polynomial.

Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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