glever

Arguments

E, A

two real square matrices of same dimensions

s

character string (default value 's')

Bfs,Bis

two polynomial matrices

chis

polynomial

Description

Computation of

(s*E-A)^-1

by generalized Leverrier's algorithm for a matrix pencil.

(s*E-A)^-1 = (Bfs/chis) - Bis.

chis = characteristic polynomial (up to a multiplicative constant).

Bfs = numerator polynomial matrix.

Bis = polynomial matrix ( - expansion of (s*E-A)^-1 at infinity).

Note the - sign before Bis.

Caution

This function uses cleanp to simplify Bfs,Bis and chis.

Examples

s=%s;F=[-1,s,0,0;0,-1,0,0;0,0,s-2,0;0,0,0,s-1];
[Bfs,Bis,chis]=glever(F)
inv(F)-((Bfs/chis) - Bis)

See also

• rowshuff — shuffle algorithm
• det — determinant
• invr — inversion of (rational) matrix
• coffg — Co-factors of a matrix of polynomials or rationals
• pencan — canonical form of matrix pencil
• penlaur — Laurent coefficients of matrix pencil