Dual list: Difference between revisions
Cmloegcmluin (talk | contribs) →Examples: use templates |
Cmloegcmluin (talk | contribs) →Examples: clarify what's happening in the first example |
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Dulist([{{map|31 49 72 87 107}}, {{map|41 65 95 115 142}}, {{map|72 114 167 202 249}}]) = [{{vector|-3 2 -1 2 -1}}, {{vector|-2 -3 -1 2 1}}, {{vector|-2 0 3 -3 1}}] | Dulist([{{map|31 49 72 87 107}}, {{map|41 65 95 115 142}}, {{map|72 114 167 202 249}}]) = [{{vector|-3 2 -1 2 -1}}, {{vector|-2 -3 -1 2 1}}, {{vector|-2 0 3 -3 1}}] | ||
In this first example, the mapping contains a redundant row; the third row is a linear combination of the other two (31+41=72, 49+65=114, etc.). Therefore, the dual list operation returns a comma basis with nullity 3, because the rank is truly 2 (and the rank and nullity must sum to the dimensionality, which is 5 here, because there are 5 terms in each map and comma, i.e. it is 11-limit). | |||
Dulist([{{vector|-3 2 -1 2 -1}}, {{vector|-2 -3 -1 2 1}}, {{vector|-2 0 3 -3 1}}]) = [{{map|1 1 3 3 2}}, {{map|0 6 -7 -2 15}}] | Dulist([{{vector|-3 2 -1 2 -1}}, {{vector|-2 -3 -1 2 1}}, {{vector|-2 0 3 -3 1}}]) = [{{map|1 1 3 3 2}}, {{map|0 6 -7 -2 15}}] | ||
Dulist([{{map|1 1 3 3 2}}, {{map|0 6 -7 -2 15}}]) = [{{vector|-3 2 -1 2 -1}}, {{vector|-2 -3 -1 2 1}}, {{vector|-2 0 3 -3 1}}] | Dulist([{{map|1 1 3 3 2}}, {{map|0 6 -7 -2 15}}]) = [{{vector|-3 2 -1 2 -1}}, {{vector|-2 -3 -1 2 1}}, {{vector|-2 0 3 -3 1}}] | ||