Actually so little use is made of vector spaces that it can be provided here. This is a good start on vector spaces, however.

We say that x is a linear combination of variables {xj} if there are constants {bj} such that x = Σj xjbj. In the proof at hand j ranges from 0 thru 1023.

In the proof at hand we are concerned with linear combinations of the 1024 complex input values. We will see that each value of a complex identifier is a LC of these inputs. The constants of the LC do not, of course depend on the inputs. They really are specific complex constants!

The only thing that we must note about linear combinations (LC) is that if x is a LC and c is a constant then cx is a LC. Further if x and y are LCs, then x+y is an LC.