Groups, Matrices, and Vector Spaces pp 297-317 | Cite as

# Unitary Diagonalization and Quadratic Forms

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## Abstract

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.

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