In the theory of LINEAR MAPS [I.3 §4.2], or *operators*, on a VECTOR SPACE [I.3 §2.3], the notions of EIGENVALUE AND EIGENVECROR [I.3 §4.3] play an important role. Recall that if *V* is a vector space (over or ) and if *T* : *V* → *V* is a linear mapping, then an *eigenvector* of *T* is a nonzero vector *e* in *V* such that *T*(*e*) = *λe* for some scalar λ then λ is the *eigenvalue* corresponding to the eigenvector *e.* If V is finite dimensional, then the eigenvalues are also the roots of the *characteristic polynomial χ*(*t*) = det(*tI* – *T*

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