Related Matrices

The companion matrix of a monic linear differential operator Dⁿ + a_{n - 1}D^{n - 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.

> 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]