Editing Hadamard matrix (section)

==Generalizations==
One basic generalization is a [[weighing matrix]]. A weighing matrix is a square matrix in which entries may also be zero and which satisfies <math>WW^\textsf{T} = wI</math> for some w, its weight. A weighing matrix with its weight equal to its order is a Hadamard matrix.<ref name="Geramita1974">{{cite journal | last1=Geramita | first1=Anthony V. | last2=Pullman | first2=Norman J. | last3=Wallis | first3=Jennifer S. | title=Families of weighing matrices | journal=Bulletin of the Australian Mathematical Society | publisher=Cambridge University Press (CUP) | volume=10 | issue=1 | year=1974 | issn=0004-9727 | doi=10.1017/s0004972700040703 | pages=119–122| s2cid=122560830 | url=https://ro.uow.edu.au/infopapers/956 }}</ref>

Another generalization defines a [[complex Hadamard matrix]] to be a matrix in which the entries are complex numbers of unit [[Complex number#Polar complex plane|modulus]] and which satisfies ''H H<sup>*</sup> = n I<sub>n</sub>'' where ''H<sup>*</sup>'' is the [[conjugate transpose]] of ''H''. Complex Hadamard matrices arise in the study of [[operator algebra]]s and the theory of [[quantum computation]].
[[Butson-type Hadamard matrices]] are complex Hadamard matrices in which the entries are taken to be ''q''<sup>th</sup> [[roots of unity]]. The term ''complex Hadamard matrix'' has been used by some authors to refer specifically to the case ''q'' = 4.