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  • John B. Kelly (a1)

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Let P be a finite set with p objects oj, j = 1, 2, … , p, and let {Si}, i = 1, 2, … , n, be a family of n subsets of P. The incidence matrix A = (aij ) for the family {Si} is defined by the rules: aij = 1 if 0j, ∈ Si and aij = 0 if 0j Si . Then, if AAT = B = (bij) (where AT denotes the transpose of A), it is easy to see that bij = |Si Sj |, i = 1, … , n, j = 1, … , n, so that the elements of B are integers with bii bij ⩾ 0.

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References

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1. Boole, George, Of propositions numerically definite (1868), Chapter IV of Studies in logic and probability (La Salle, 111. 1952).
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