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Справка Scilab >> Linear Algebra > Matrix Pencil > glever

glever

inverse of matrix pencil

Syntax

[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
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Last updated:
Tue Feb 14 15:13:21 CET 2017