MyWikiBiz, Author Your Legacy — Friday September 27, 2024
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, 02:50, 27 February 2008
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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%" | | {| 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''. |
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| 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: |
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| : ''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'')). |
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− | 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. |
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| Consequently, we have the result: | | Consequently, we have the result: |