Scilab Home page | Wiki | Bug tracker | Forge | Mailing list archives | ATOMS | File exchange
Scilab 6.0.2
Change language to: English - Français - Português - 日本語 -

# inv

matrix inverse

`inv(X)`

### Arguments

X

real or complex square matrix, polynomial matrix, rational matrix in transfer or state-space representation.

### Description

`inv(X)` is the inverse of the square matrix `X`. A warning message is printed if `X` is badly scaled or nearly singular.

For polynomial matrices or rational matrices in transfer representation, `inv(X)` is equivalent to `invr(X)`.

`inv([])` returns `[]`.

For linear systems in state-space representation (`syslin` list), `invr(X)` is equivalent to `invsyslin(X)`.

### References

`inv` function for matrices of numbers is based on the Lapack routines DGETRF, DGETRI for real matrices and ZGETRF, ZGETRI for the complex case. For polynomial matrix and rational function matrix `inv` is based on the `invr` Scilab function.

### Examples

```A=rand(3,3);inv(A)*A

x=poly(0,'x');
A=[x,1,x;x^2,2,1+x;1,2,3];inv(A)*A

A=[1/x,2;2+x,2/(1+x)]
inv(A)*A

A=ssrand(2,2,3);
W=inv(A)*A
clean(ss2tf(W))```

• slash — (/) правое деление и обратная связь
• backslash — (\) левое матричное деление.
• pinv — pseudoinverse
• qr — QR decomposition
• lufact — sparse lu factorization
• lusolve — sparse linear system solver
• invr — inversion of (rational) matrix
• coff — resolvent (cofactor method)
• coffg — Co-factors of a matrix of polynomials or rationals