Canonical mxtrace_linear := Linear mxtrace_is_scalar.

(* Specifications: *)
Lemma mxtrace0 : \tr 0 = 0. Proof. exact: raddf0. Qed.
Lemma mxtraceD A B : \tr (A + B) = \tr A + \tr B. Proof. exact: raddfD. Qed.
Lemma mxtraceZ a A : \tr (a *: A) = a * \tr A. Proof. exact: scalarZ. Qed.
Lemma mxtrace_diag D : \tr (diag_mx D) = \sum_j D 0 j.
Lemma mxtrace1 : \tr 1%:M = n%:R. Proof. exact: mxtrace_scalar. Qed.
End Trace.