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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Carrell, J.B. (2017). Unitary Diagonalization and Quadratic Forms. In: Groups, Matrices, and Vector Spaces. Springer, New York, NY. https://doi.org/10.1007/978-0-387-79428-0_9
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DOI: https://doi.org/10.1007/978-0-387-79428-0_9
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