Why are these column vectors orthogonal in mod 5 ?

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

Question

Why are these column vectors orthogonal in mod 5 ?

$$\begin{bmatrix} 2^0&2^0&2^0&2^0\2^0&2^1&2^2&2^3\2^0&2^2&2^4&2^6\2^0&2^3&2^6&2^9\ \end{bmatrix}$$

ganeshie8 · Answer

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

kainui · Answer

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

kainui · Answer

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