Editing Hadamard matrix (section)

===Regular Hadamard matrices===
[[Regular Hadamard matrices]] are real Hadamard matrices whose row and column sums are all equal. A necessary condition on the existence of a regular ''n''&thinsp;×&thinsp;''n'' Hadamard matrix is that ''n'' be a [[square number]]. A [[circulant]] matrix is manifestly regular, and therefore a circulant Hadamard matrix would have to be of square order. Moreover, if an ''n''&thinsp;×&thinsp;''n'' circulant Hadamard
matrix existed with ''n'' > 1 then ''n'' would necessarily have to be of the form 4''u''<sup>2</sup> with ''u'' odd.<ref>{{cite journal |first=R. J. |last=Turyn |title=Character sums and difference sets |journal=[[Pacific Journal of Mathematics]] |volume=15 |issue=1 |pages=319–346 |year=1965 |mr=0179098 |doi=10.2140/pjm.1965.15.319|doi-access=free }}</ref><ref>{{cite book |first=R. J. |last=Turyn |chapter=Sequences with small correlation |editor-first=H. B. |editor-last=Mann |title=Error Correcting Codes |publisher=Wiley |location=New York |year=1969 |pages=195–228 }}</ref>