Say I have a set of vectors, $v_{0\ldots n}$, all of which are orthogonal to each other and all of which are of length $m$.
If I took a portion of each vector (same start and end indices for each), would those portions also be orthogonal to each other?
e.g. would $v_0\left[0:\frac m2\right]$, $v_1\left[0:\frac m2\right]$, $v_2\left[0:\frac m2\right]$, etc. all be orthogonal to each other, and if so, does that hold true regardless of the start and end indices (as long as they're consistent)?
Apologies for the mathematical notation, I'm not certain how to represent a subset/slice of a vector properly, so I wrote it the way we do in software.
No. Take $v_1=(1,1,0)$ and $v_2=(1,-1,0)$. Are [taking only first and third coordinates] $(1,0)$ and $(1,0)$ orthogonal to each other?