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Butson-type Hadamard Matrices
In mathematics, a complex Hadamard matrix ''H'' of size ''N'' with all its columns (rows) mutually orthogonal, belongs to the Butson-type ''H''(''q'', ''N'') if all its elements are powers of ''q''-th root of unity, :: (H_)^q = 1 \quad\text\quad j,k = 1,2,\dots,N. Existence If ''p'' is prime and N>1, then H(p,N) can exist only for N = mp with integer ''m'' and it is conjectured they exist for all such cases with p \ge 3. For p=2, the corresponding conjecture is existence for all multiples of 4. In general, the problem of finding all sets \ such that the Butson-type matrices H(q,N) exist, remains open Open or OPEN may refer to: Music * Open (band), Australian pop/rock band * The Open (band), English indie rock band * ''Open'' (Blues Image album), 1969 * ''Open'' (Gerd Dudek, Buschi Niebergall, and Edward Vesala album), 1979 * ''Open'' (Go .... Examples *H(2,N) contains real Hadamard matrices of size ''N'', *H(4,N) contains Hadamard matrices composed of \pm 1, \p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
