proposition: Lemma trowb_is_linear n1 m2 n2 (B : 'M_(m2,n2)) : linear (@trowb n1 m2 n2 B).
proof: Proof. elim: n1=> [|n1 IH] //= k A1 A2 /=; first by rewrite scaler0 add0r. rewrite linearD /= linearZ. - apply/matrixP=> i j. rewrite !mxE. case: split=> a. by rewrite !mxE mulrDl mulrA. by rewrite linearD /= linearZ IH !mxE. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype choice ssrnat seq) mathcomp(path div fintype tuple finfun bigop prime order) mathcomp(ssralg poly finset gproduct fingroup morphism) mathcomp(perm automorphism quotient finalg action zmodp) mathcomp(commutator cyclic center pgroup nilpotent sylow) mathcomp(abelian matrix mxalgebra mxpoly mxrepresentation) mathcomp(vector ssrnum algC classfun archimedean)