Defactoring: Difference between revisions
Cmloegcmluin (talk | contribs) |
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\end{array} \right]</math> | \end{array} \right]</math> | ||
The pivots are 1 and 11, so that 11 tells us that we had a common factor of 11. You could say that the HNF is useful for identifying common factors, but not for removing them. But if you leave them behind in the column-style HNF, the information that is retained in the unimodular matrix which is the other product of the Hermite decomposition, is enough to preserve everything important about the temperament, to get you back to where you started via an inverse and a trimming of extraneous rows. | The pivots are 1 and 11, so that 11 tells us that we had a common factor of 11<ref>In the doubly-enfactored case of {{vector|{{map|17 16 -4}} {{map|4 -4 1}}}}, i.e. with a common factor of 33 = 3 × 11, the two pivots of the HNF are 3 and 11, putting each of them on display separately.</ref>. You could say that the HNF is useful for identifying common factors, but not for removing them. But if you leave them behind in the column-style HNF, the information that is retained in the unimodular matrix which is the other product of the Hermite decomposition, is enough to preserve everything important about the temperament, to get you back to where you started via an inverse and a trimming of extraneous rows. | ||
== other details to report == | == other details to report == | ||