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# inv

matrix inverse

### Syntax

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

### See also

- slash — (/) right divisions. System's feed back. Comments
- backslash — (\) left matrix division.
- 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

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