# `inv`

_Matrix inverse_


```syntax
inv x     inv[x]
```

Returns the inverse of non-singular float matrix `x`.
```q
q)a:3 3#2 4 8 3 5 6 0 7 1f
q)inv a
-0.4512195  0.6341463  -0.195122
-0.03658537 0.02439024 0.1463415
0.2560976   -0.1707317 -0.02439024
q)a mmu inv a
1 2.220446e-16 -2.775558e-17
0 1            5.551115e-17
0 0            1
q)1=a mmu inv a
100b
010b
001b
```


`lsq` solves a normal equations matrix via Cholesky decomposition – solving systems is more robust than matrix inversion and multiplication.

Since V3.6 2017.09.26 `inv` uses LU decomposition.
Previously it used Cholesky decomposition as well.


---- 

[`lsq`](lsq.md)


[Mathematics](../basics/math.md)


[LU decomposition](https://en.wikipedia.org/wiki/LU_decomposition "Wikipedia"),
[Cholesky decomposition](https://en.wikipedia.org/wiki/Cholesky_decomposition#Matrix_inversion "Wikipedia")