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Scilab Help >> 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)```

• 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