Related Matrices

The companion matrix of a monic linear differential operator Dn + an - 1Dn - 1 + ... + a0 ∈F[D] is defined as the n x n matrix

CompanionMatrix(L) : RngDiffOpElt -> AlgMatElt
Returns the companion matrix of the monic differential operator L.

Example RngDiff_example-companion-matrix (H118E55)

> F<z> := RationalDifferentialField(Rationals());
> R<D> := DifferentialOperatorRing(F);
> L := D^3-z*D^2+2*D+5;
> CompanionMatrix(L);
[0 1 0]
[0 0 1]
[-5 -2 z]
V2.28, 13 July 2023