# The article “Vector reconstruction from Firing Rates” of Abbott and Salinas

I am reading it, and it is basically very clear. But still, some points are not clear to me.

For example, how is equation (7.1) in page 12:

$Q_{i,j}^{-1} = F(\overline C_i \overline C_j)$

It it said there that

"By rotational invariance, the correlation matrix element $Q_{i,j}$ and the corresponding inverse element $Q_{i,j}^{-1}$ can only depend on $\overline C_i \cdot \overline C_j$".

Does anyone here, by any chance, know what is "rotational invariance"?

Thank you!

What they mean is that as long as you rotate $C_i$ and $C_j$ by the same amount, the dot product will be the same. This is rotational invariance because the dot product is invariant to coherent rotation of the relevant vectors.