Calculate the inverse of a matrix

Hello, i want to calculate the reverse of this matrix :

 1    -1     0     0
-1     1     0     0
 0     0     1    -1
 0     0    -1     1

but I get the following result :

   Inf   Inf   Inf   Inf
   Inf   Inf   Inf   Inf
   Inf   Inf   Inf   Inf
   Inf   Inf   Inf   Inf

what are your suggestion? Thanks.

[Adam]

What do you expect to get?

[Brendan Hamm]

This is a singular matrix, as can be seen by the linear dependence of columns:

X(:,1) == -X(:,2)

and

X(:,3) == -X(:,4)

[amine&&]

Thanks Brendan. Yes i understand you're is a singular matrix, therefore its inverse can not calculate but we can calculate a pseudo-inverse.

Answer 1

[John D'Errico]

This is a singular matrix. No matter how badly you want to do so, you cannot invert a singular matrix. Not possible. Never will be. The laws of mathematics are simple in this respect. The inverse does not exist. You cannot form what does not exist.

At best, you can use pinv, to compute a pseudo-inverse. It is NOT an inverse. It does not have the properties of an inverse.

[amine&&]

Ok John. thanks!

[Valentin Marinov]

But you can imagine it exist and call it imaginary if you really want to, right haha?

P.S.: it's a joke.

[John D'Errico]

Yes, I understand you were joking. The inverse really does not exist for a truly singular matrix. This is the same thing as asking what is the value of 1/0. That value is undefined, not truly inf. But the best that MATLAB can do is to call it inf.

>> 1/0
ans =
   Inf
   
>> A = [ 1    -1     0     0
-1     1     0     0
 0     0     1    -1
 0     0    -1     1];

>> inv(A)
Warning: Matrix is singular to working precision. 
 
ans =
   Inf   Inf   Inf   Inf
   Inf   Inf   Inf   Inf
   Inf   Inf   Inf   Inf
   Inf   Inf   Inf   Inf

[amine&&]

@Valentin Marinov thanks for the joke. Can you give the definition of the Moore–Penrose inverse.

[Valentin Marinov]

Sure. Here's a video that explains it good enough: https://www.youtube.com/watch?v=5bxsxM2UTb4. The example is at 3:30. I'm no pro so don't think I know how to use this in real life, but the guy explains the idea pretty good and tells the matlab funtions, you can use to simulate the actions he explains. Hope it helps you out.

EDIT: just saw the post is from 2016, so I assume you don't need that anymore, but I'll leave it just in case.