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m Reverted edits by 122.151.61.45 (talk) to last version by Dedhert.Jr |
Presumably "magma" refers to the algebraic structure, not molten rock. |
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For a given relation ''R'', a maximal rectangular relation contained in ''R'' is called a concept in ''R''. Relations may be studied by decomposing into concepts, and then noting the [[heterogeneous relation#Induced concept lattice|induced concept lattice]].
Consider the table of group-like structures, where "unneeded" can be denoted 0, and "required" denoted by 1, forming a logical matrix <math>R .</math> To calculate elements of <math>RR^{\operatorname{T}}</math>, it is necessary to use the logical inner product of pairs of logical vectors in rows of this matrix. If this inner product is 0, then the rows are orthogonal. In fact, [[small category]] is orthogonal to [[quasigroup]], and [[groupoid]] is orthogonal to [[Magma (algebra)|magma]]. Consequently there are zeros in <math>RR^{\operatorname{T}}</math>, and it fails to be a [[universal relation]].
==Row and column sums==
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