In linear algebra, a matrix is orthogonal if each row is perpendicular to every other row. This can be brute force tested by taking the dot product of every pair distinct rows, and ensuring that the result is zero in each case. Some orthogonal matrices:

[ 1 0 0 0 ] [ -2 4 0 ] [ 3-2i 13 ]
[ 0 1 0 0 ] [ 2 -1 0 ] [ 3+2i -1 ]
[ 0 0 1 0 ] [ 0 0 3 ]
[ 0 0 0 1 ]