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→Matrix representation: binding expressions
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Stripping down to the bare essentials, one obtains the matrices of coefficients for the relations ''G'' and ''H'':
Stripping down to the bare essentials, one obtains the following matrices of coefficients for the relations ''G'' and ''H''.
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{| style="text-align:center; width=30%"
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These are the logical matrix representations of the 2-adic relations ''G'' and ''H''.
These are the logical matrix representations of the 2-adic relations ''G'' and ''H''.
If the 2-adic relations ''G'' and ''H'' are viewed as logical sums, then their relational composition ''G'' ο ''H'' can be regarded as a product of sums, a fact that can be indicated as follows:
If the 2-adic relations ''G'' and ''H'' are viewed as logical sums, then their relational composition ''G'' ο ''H'' can be regarded as a product of sums, a fact that can be indicated as follows:
: ''G'' ο ''H'' = (∑<sub>''ik''</sub> ''G''<sub>''ik''</sub>(''i'':''k''))(∑<sub>''kj''</sub> ''H''<sub>''kj''</sub>(''k'':''j'')).
: ''G'' ο ''H'' = (∑<sub>''ik''</sub> ''G''<sub>''ik''</sub>(''i'':''k''))(∑<sub>''kj''</sub> ''H''<sub>''kj''</sub>(''k'':''j'')).
A moment's thought will tell us that (''G'' ο ''H'')<sub>''ij''</sub> = 1 if and only if there is an element ''k'' in ''X'' such that ''G''<sub>''ik''</sub> = 1 and ''H''<sub>''kj''</sub> = 1.
A moment's thought will tell us that (''G'' ο ''H'')<sub>''ij''</sub> = 1 if and only if there is an element ''k'' in ''X'' such that ''G''<sub>''ik''</sub> = 1 and ''H''<sub>''kj''</sub> = 1.
Consequently, we have the result:
Consequently, we have the result: