Scilab Home page | Wiki | Bug tracker | Forge | Mailing list archives | ATOMS | File exchange
Please login or create an account
Scilab-Branch-6.1-GIT
Change language to: English - Français - Português - 日本語 -
Справка Scilab >> Linear Algebra > 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 — определитель квадратной матрицы
• invr — inverts a matrix of polynomials or of rationals
• coffg — Co-factors of a matrix of polynomials or rationals
• pencan — canonical form of matrix pencil
• penlaur — Laurent coefficients of matrix pencil

### Comments

Add a comment:
Please login to comment this page.

 Report an issue << fstair pencil kroneck >>

 Scilab EnterprisesCopyright (c) 2011-2017 (Scilab Enterprises)Copyright (c) 1989-2012 (INRIA)Copyright (c) 1989-2007 (ENPC)with contributors Last updated:Mon Jan 03 14:39:53 CET 2022