# 6x6 matrix NullSpace

I'm working with a 6x6 matrix. Whenever I try to find the NullSpace and FullSimplify it, I get the error

No more memory available. Mathematica kernel has shut down. Try quitting other applications and then retry.

When trying the exact same approach with a simular matrix that, in my mind, looks more difficult, is works without a problem. Here is the matrix that works:

{
{
-(1/(1 + E^(EA2 + Vca - μ))) - E^μ/(E^ED1 + E^μ),
1/(1 + E^(-ED1 + μ)),
0,
1/(1 + E^(-EA2 - Vca + μ)),
0,
0
},
{
1/(1 + E^(ED1 - μ)),
-1 - 2/(-1 + E^(-ED1 + ED2)) - 2/(-1 + E^(EA2 - ED1 + Vca)) +
1/(1 + E^(ED1 - μ)) - E^μ/(E^EA2 + E^μ),
(2 E^ED2)/(-E^ED1 + E^ED2),
2 (1 + 1/(-1 + E^(EA2 - ED1 + Vca))),
1/(1 + E^(-EA2 + μ)),
0
},
{
0,
2/(-1 + E^(-ED1 + ED2)),
-3 - 2/(-1 + E^(-ED1 + ED2)) + 1/(1 + E^(-EA2 + ED2 - Vca)) -
E^μ/(E^EA2 + E^μ),
1/(1 + E^(-EA2 + ED2 - Vca)),
0,
1/(1 + E^(-EA2 + μ))
},
{
1/(1 + E^(EA2 + Vca - μ)),
2/(-1 + E^(EA2 - ED1 + Vca)),
1/(1 + E^(EA2 - ED2 + Vca)),
-3 - E^(EA2 + Vca)/(E^ED2 + E^(EA2 + Vca)) -
2/(-1 + E^(EA2 - ED1 + Vca)) + 1/(1 + E^(EA2 + Vca - μ)) -
E^(Vca + μ)/(E^ED1 + E^(Vca + μ)),
1/(1 + E^(-ED1 + Vca + μ)),
0
},
{
0,
1/(1 + E^(EA2 - μ)),
0,
1/(1 + E^(ED1 - Vca - μ)),
-2 - 2/(-1 + E^(-ED1 + ED2)) + 1/(1 + E^(EA2 - μ)) +
1/(1 + E^(ED1 - Vca - μ)),
(2 E^ED2)/(-E^ED1 + E^ED2)},
{
0,
0,
1/(1 + E^(EA2 - μ)),
0,
2/(-1 + E^(-ED1 + ED2)),
-3 - 2/(-1 + E^(-ED1 + ED2)) + 1/(1 + E^(EA2 - μ))
}
}


and here is the one that doesn't work:

{
{
-(1/(1 + E^(ED1 - μl))) - 1/(1 + E^(EA2 + Vca - μr)),
1/(1 + E^(-ED1 + μl)),
0,
1/(1 + E^(-EA2 - Vca + μr)),
0,
0
},
{
1/(
1 + E^(ED1 - μl)),
-1 + 1/(1 - E^((-ED1 + ED2)/Ts)) + 1/(
1 - E^(EA2 - ED1 + Vca)) + 1/(1 - E^((EA2 - ED1 + Vca)/Ts)) +
1/(1 + E^(ED1 - μl)) - 1/(1 + E^(EA2 - μr)),
1 + 1/(-1 + E^((-ED1 + ED2)/Ts)),
1/(-1 + E^((EA2 - ED1 + Vca)/Ts)),
1/(1 + E^(-EA2 + μr)),
0
},
{
0,
1/(-1 + E^((-ED1 + ED2)/Ts)),
-2 + 1/(1 - E^((-ED1 + ED2)/Ts)) + 1/(1 + E^(-EA2 + ED2 - Vca)) -
1/(1 + E^(EA2 - μr)),
1/(1 + E^(-EA2 + ED2 - Vca)),
0,
1/(1 + E^(-EA2 + μr))
},
{
1/(1 + E^(EA2 + Vca - μr)),
1/(-1 + E^(EA2 - ED1 + Vca)) + 1/(-1 + E^((EA2 - ED1 + Vca)/Ts)),
1/(1 + E^(EA2 - ED2 + Vca)),
-3 - 1/(1 + E^(-EA2 + ED2 - Vca)) + 1/(1 - E^(EA2 - ED1 + Vca)) +
1/(1 - E^((EA2 - ED1 + Vca)/Ts)) - 1/(1 + E^(ED1 - Vca - μl)) +
1/(1 + E^(EA2 + Vca - μr)),
1/(1 + E^(-ED1 + Vca + μl)),
0
},
{
0,
1/(1 + E^(EA2 - μr)),
0,
1/(1 + E^(ED1 - Vca - μl)),
-2 + 1/(1 - E^((-ED1 + ED2)/Ts)) + 1/(1 + E^(ED1 - Vca - μl)) +
1/(1 + E^(EA2 - μr)),
1 + 1/(-1 + E^((-ED1 + ED2)/Ts))
},
{
0,
0,
1/(1 + E^(EA2 - μr)),
0,
1/(-1 + E^((-ED1 + ED2)/Ts)),
-2 + 1/(1 - E^((-ED1 + ED2)/Ts)) + 1/(1 + E^(EA2 - μr))
}
}


I'm using the following code:

eqvector = FullSimplify[NullSpace[m][[1]]];
Zeq = FullSimplify[Sum[eqvector[[i]], {i, 1, 6}]];
eqvector = FullSimplify[eqvector/Zeq]


the code works for the first matrix, but not for the second. Does anybody have any idea of what I can do?

-
First you should write the matrix clearly. Then i can known your problem! –  howard Apr 7 at 12:11
Welcome to the site @Philip. I've edited your post, but you can do it for yourself: use Ctrl-K to format blocks of text as code. –  István Zachar Apr 7 at 13:35
The problem is not with finding the NullSpace for the second matrix but to FullSimplify it. With Simplify, I can get an answer, and timings show that simplifying the first element of eqvector is the most consuming (~111 sec) while the last one took 6 sec. –  István Zachar Apr 7 at 14:13