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Obviously, the condition to have exactly one 0 on each row and column is a consequence of CC'=(n-1)I, (since diagonal elements are sum( Cij^2 , j=1..n) for any given i) but there are research papers that do not require the 0 to be on the diagonal, e.g.
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Definition 3.1 A weighing matrix W(n,w) of weight w!=0 and order n is a square matrix of size n with entries from {−1, 0, +1} satisfying WW^t = wI. A W(n, n) is called an
Hadamard matrix of order n, a W(n, n−1) is called a conference matrix of order
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A conference matrix C of order n is a square (0,±1) matrix of side n with exactly one 0 in every row and every column such that CC' = (n−1)I , where I is the identity matrix and C' denotes the transpose of
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The intro mentions some uses of conference matrices with references but wouldn't it be better to have a short section that explains uses? If someone has time to do it, that would be nice!
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I have reversed the bold-facing of the matrix names, which seems to be due to a misunderstanding. The "C" in C-matrix is not a matrix, it is the abbreviation of the word "conference".
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Can anyone add to the introduction more information about what conference matrices are used for, and how?
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A possibility of such a matrix which does not have the 0 on the diagonal is:
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If both definitions are used, it should be mentioned. —
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