Kunze Linear Algebra · Problem 7.4.2

Rational and Jordan Forms

Mathematics — Methods · cyclic-vector-invariant-factors

Problem

Let TT be a linear operator on a finite-dimensional vector space and let AA be the matrix of TT in some ordered basis. Then TT has a cyclic vector if and only if the determinants of the (n−1)×(n−1)(n-1) \times (n-1) submatrices of xI−AxI - A are relatively prime.

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