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Scilab Help >> Polynomials > invr

# invr

inverts a matrix of polynomials or of rationals

### Syntax

`F = invr(H)`

### Arguments

H

polynomial or rational matrix

F

polynomial or rational matrix

### Description

`invr` computes `H-1` using Leverrier's algorithm (see function's code).

### Examples

```s = %s;
H = [s, s*s+2 ; 1-s, 1+s], iH = invr(H), H * iH

[Num,den] = coffg(H); Num/den
H = [1/s, (s+1) ; 1/(s+2), (s+3)/s]; invr(H)```
```--> H = [s, s*s+2 ; 1-s, 1+s], iH = invr(H), H * iH
H  =
s     2 +s²
1 -s  1 +s

iH  =
1 +s       -2 -s²
----------  ----------
-2 +3s +s³  -2 +3s +s³

-1 +s         s
----------  ----------
-2 +3s +s³  -2 +3s +s³

ans  =
1  0
-  -
1  1

0  1
-  -
1  1

--> [Num,den] = coffg(H); Num/den
ans  =
1 +s       -2 -s²
----------  ----------
-2 +3s +s³  -2 +3s +s³

-1 +s         s
----------  ----------
-2 +3s +s³  -2 +3s +s³
```

• inv — matrix inverse
• glever — inverse of matrix pencil
• coffg — Co-factors of a matrix of polynomials or rationals