Dear all,

I am trying to do the following: Given I have some column vector of shape (5 x 1) I want to calculate the inverse of (q @ q.t()). This actually shouldn’t be such a difficult task, however, it seems that the inverse of this expression, torch.inverse(q @ q.t()) is way off:

```
In [358]: q = torch.randn(5,1)
In [359]: q
Out[359]:
tensor([[ 0.2144],
[ 0.2899],
[-1.0016],
[-2.5544],
[ 0.3549]])
In [360]: (q @ q.t()) @ torch.inverse(q @ q.t())
Out[360]:
tensor([[ 0.2019, -1.0537, 0.2293, -0.3905, -0.7937],
[-0.2614, -0.9735, 0.2418, -0.4921, -1.4343],
[ 0.4410, 7.5348, 0.6504, 1.9400, 3.7739],
[ 4.5718, 17.0569, -1.1591, 4.7328, 12.1593],
[ 0.3166, -1.8443, 0.1681, -0.5732, -0.4462]])
```

So this calculation should obviously return something which is close to the identity. So is this some numerical issue?

If I just create a (5 x 5) matrix via w = torch.randn(5,5) and then calculate (w @ w.t()) @ torch.inverse(w @ w.t()) there is no issue and the result is close to the identity.

So is there something special by matrix multiplying a column vector with its transpose to obtain a matrix?

So maybe what I am missing is that q @ q.t() is often singular or close to singular? And hence the inverse is actually not defined?

Best regards