Butson-type Hadamard matrix
In mathematics, a complex [Hadamard matrix] H of size N with all its columns mutually orthogonal, belongs to the Butson-type H if all its elements are powers of q-th root of unity,
Existence
If p is prime and, then can existonly for with integer m and
it is conjectured they exist for all such cases
with. For, the corresponding conjecture is existence for all multiples of 4.
In general, the problem of finding all sets
such that the Butson-type matrices
exist, remains open.
Examples
- contains real Hadamard matrices of size N,
- contains Hadamard matrices composed of – such matrices were called by Turyn, complex Hadamard matrices.
- in the limit one can approximate all complex Hadamard matrices.
- Fourier matrices