Question

Why are these column vectors orthogonal in mod 5 ?

\[\begin{bmatrix} 2^0&2^0&2^0&2^0\\2^0&2^1&2^2&2^3\\2^0&2^2&2^4&2^6\\2^0&2^3&2^6&2^9\\ \end{bmatrix}\]

Answer 1

\[\LARGE \begin{bmatrix} 2^0&2^0&2^0&2^0\\2^0&2^1&2^2&2^3\\2^0&2^2&2^4&2^6\\2^0&2^3&2^6&2^9\\ \end{bmatrix}\]

Answer 2

2 is a generator of the cyclic group with 4 elements in it, that's part of the reason, if we wanted we could replace 2 with i (the complex number) and get the same result :P

Answer 3

Pick any 4 numbers with about 6 digits or less, I'll show you something cool.