glever

inverse of matrix pencil

Calling Sequence

[Bfs,Bis,chis]=glever(E,A [,s])

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 inverse of polynomial matrix
• pencan canonical form of matrix pencil
• penlaur Laurent coefficients of matrix pencil