You should better provide concrete examples so that we understand your question.

Let us first create a 3 by 3 random matrix:

```
sage: m = random_matrix(QQ,3,3) ; m
[ -2 1 -2]
[ 0 0 -2]
[ 0 0 -1/2]
```

We can find its eigenvalues:

```
sage: L = m.eigenvalues() ; L
[0, -1/2, -2]
```

Then, if the interesting one is `-1/2`

, let us find its position in the list:

```
sage: L.index(-1/2)
1
```

According to the documentatnion of `m.eigenvectors_right`

, we can find the list of rignt eigenvectors as a list of tuples "`(e,V,n)`

where e is the eigenvalue, V is a list of eigenvectors forming a basis for the corresponding right eigenspace, and n is the algebraic multiplicity of the eigenvalue.":

```
sage: m.eigenvectors_right()
[(0, [
(1, 2, 0)
], 1), (-1/2, [
(1, 3, 3/4)
], 1), (-2, [
(1, 0, 0)
], 1)]
```

The are ordered in the same way as with `m.eigenvalues()`

, so we can find the tuple associated to the eigenvalue `-1/2`

as follows;

```
sage: m.eigenvectors_right()[L.index(-1/2)]
(-1/2, [
(1, 3, 3/4)
], 1)
```

We want an eigenvector, so the second entry (with index 1) of this tuple is interesting:

```
sage: m.eigenvectors_right()[L.index(-1/2)][1]
[
(1, 3, 3/4)
]
```

SInce we do only want one eigenvector (not the whole basis), let us pick the first entry (with index 0):

```
sage: m.eigenvectors_right()[L.index(-1/2)][1][0]
(1, 3, 3/4)
```