## eliminate the nullspace of a matrix

### Ano (view profile)

on 7 Aug 2017
Latest activity Commented on by Torsten

on 7 Aug 2017

### Azzi Abdelmalek (view profile)

Hello, how can I eliminate the nullspace of a square matrix using Matlab? Thank you!

John D'Errico

### John D'Errico (view profile)

on 7 Aug 2017

Sorry, but eliminating the nullspace of a matrix has no meaning, just some jargon that you have made up. Define carefully what you want to do. Only you know that.

A matrix has a nullspace. That null space may be empty or not. But you cannot "eliminate" it. So what do you want to do?

Torsten

### Torsten (view profile)

on 7 Aug 2017

If you want a basis of the row space of A, use orth(A.').

The rule is that

```null(A) + orth(A.') = R^n
```

where n is the dimension of your matrix.

Best wishes

Torsten.

### Azzi Abdelmalek (view profile)

on 7 Aug 2017

If you have any matrix, square or not, you have only one possibility: remove entire rows or columns that are equal to zero

Example

```A=[1 2 3 0;0 0 0 0;1 4 5 0 ;2 7 8 0]
ix=~any(A,1)
A(:,ix)=[]
iy=~any(A,2)
A(iy,:)=[]
```