# The minimum of a matrix

So I have been writing some code using Sage, which by the way is awesome so far. And I had some simple check to do, i.e. all elements of some matrices have to be nonnegative. So I figured I would just see if the minimum of these matrices is nonnegative. In programms like matlab this is usualy achieved by min(min(A)) for some matrix A. I figured it would be the same for sage, so I tested this to be sure and everything seemed to work. But then I stumbeled upon something weird and I found this case (that is this is some of the output of the case). These are the 5 matrices followed by the minima of the same 5 matrices respectively.

```
[ 1.0000 0.00000 0.00000 0.00000 0.00000]
[0.00000 3.0000 0.00000 0.00000 0.00000]
[0.00000 0.00000 10.000 0.00000 0.00000]
[0.00000 0.00000 0.00000 5.0000 0.00000]
[0.00000 0.00000 0.00000 0.00000 1.0000]
-------------------------------------------------------------
[ 0.00000 1.0000 0.00000 0.00000 0.00000]
[ 1.0000 1.0000 0.00000 0.00000 1.0000]
[ 0.00000 0.00000 4.4444 5.5556 0.00000]
[ 0.00000 0.00000 5.5556 -0.55556 0.00000]
[ 0.00000 1.0000 0.00000 0.00000 0.00000]
-------------------------------------------------------------
[0.00000 0.00000 1.0000 0.00000 0.00000]
[0.00000 0.00000 1.3333 1.6667 0.00000]
[ 1.0000 1.3333 4.4444 2.2222 1.0000]
[0.00000 1.6667 2.2222 1.1111 0.00000]
[0.00000 0.00000 1.0000 0.00000 0.00000]
-------------------------------------------------------------
[ 0.00000 0.00000 0.00000 1.0000 0.00000]
[ 0.00000 0.00000 3.3333 -0.33333 0.00000]
[ 0.00000 3.3333 4.4444 2.2222 0.00000]
[ 1.0000 -0.33333 2.2222 1.1111 1.0000]
[ 0.00000 0.00000 0.00000 1.0000 0.00000]
-------------------------------------------------------------
[0.00000 0.00000 0.00000 0.00000 1.0000]
[0.00000 3.0000 0.00000 0.00000 0.00000]
[0.00000 0.00000 10.000 0.00000 0.00000]
[0.00000 0.00000 0.00000 5.0000 0.00000]
[ 1.0000 0.00000 0.00000 0.00000 0.00000]
-----minima--------------------------------------------------
[0, 0, 0, 0, 0]
```

Now I actually have a case which is very similar, that is, it is a permutation of these set of matrices above and for those I do get the correct answers

```
[ 1.0000 0.00000 0.00000 0.00000 0.00000]
[0.00000 3.0000 0.00000 0.00000 0.00000]
[0.00000 0.00000 5.0000 0.00000 0.00000]
[0.00000 0.00000 0.00000 10.000 0.00000]
[0.00000 0.00000 0.00000 0.00000 1.0000]
-------------------------------------------------------------
[ 0.00000 1.0000 0.00000 0.00000 0.00000]
[ 1.0000 1.0000 0.00000 0.00000 1.0000]
[ 0.00000 0.00000 -0.55556 5.5556 0.00000]
[ 0.00000 0.00000 5.5556 4 ...
```