proposition: Corollary Theorem7' (m : nat) (f : 'M[R[i]]_m) : (0 < m)%N -> exists a, eigenvalue f a.
proof: Proof. case: m f => // m f _; have /Eigen1VecP := @Lemma6 m 0. move=> /(_ m.+1 1 _ f) []; last by move=> a; exists a. + by rewrite mxrank1 (contra (dvdn_leq _)) // -ltnNge ltn_expl. + by rewrite submx1. Qed.
imports: HB(structures) mathcomp.ssreflect.ssreflect mathcomp(ssrfun ssrbool eqtype ssrnat seq choice fintype) mathcomp(bigop order ssralg ssrint div ssrnum rat poly closed_field) mathcomp(polyrcf matrix mxalgebra tuple mxpoly zmodp binomial realalg) mathcomp(mxpoly)