Dual list: Difference between revisions

ArrowHead294 (talk | contribs)
mNo edit summary
ArrowHead294 (talk | contribs)
m Remove escapes as they are not needed
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In this first example, the mapping contains a redundant row; the third row is a linear combination of the other two ({{nowrap|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).
In this first example, the mapping contains a redundant row; the third row is a linear combination of the other two ({{nowrap|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).


dl[{{vector| -3 2 -1 2 -1 }}, {{vector| -2 -3 -1 2 1 }}, {{vector| -2 0 3 -3 1 }}]) {{nowrap|{{=}} {{!(}}{{map| 1 1 3 3 2 }}, {{map| 0 6 -7 -2 15 }}{{)!}}}}
dl[{{vector| -3 2 -1 2 -1 }}, {{vector| -2 -3 -1 2 1 }}, {{vector| -2 0 3 -3 1 }}]) {{nowrap|{{=}} [{{map| 1 1 3 3 2 }}, {{map| 0 6 -7 -2 15 }}]}}


dl[{{map| 1 1 3 3 2 }}, {{map| 0 6 -7 -2 15 }}]) {{nowrap|{{=}} {{!(}}{{vector| -3 2 -1 2 -1 }}, {{vector| -2 -3 -1 2 1 }}, {{vector| -2 0 3 -3 1 }}{{)!}}}}
dl[{{map| 1 1 3 3 2 }}, {{map| 0 6 -7 -2 15 }}]) {{nowrap|{{=}} [{{vector| -3 2 -1 2 -1 }}, {{vector| -2 -3 -1 2 1 }}, {{vector| -2 0 3 -3 1 }}]}}


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]
[[Category:Math]]
[[Category:Math]]