Defactoring: Difference between revisions
Cmloegcmluin (talk | contribs) helpful table |
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### show the examples we tried, like in the big defactoring table | ### show the examples we tried, like in the big defactoring table | ||
== | == relationship between various matrix echelon forms == | ||
There are several well-known echelon matrix forms. The most general form, with the fewest constraints, is simply called Row Echelon Form, or REF. It's only constraints are: | There are several well-known echelon matrix forms. The most general form, with the fewest constraints, is simply called Row Echelon Form, or REF. It's only constraints are: | ||
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# The IRREF and HNF are the same, but the RREF is different. Example: hanson. | # The IRREF and HNF are the same, but the RREF is different. Example: hanson. | ||
== | == canonical comma-bases == | ||
DC form is not only for mappings. Comma-bases — the duals of mappings — may also be put into DC form, as long as they are first antitransposed<ref>See a discussion of the antitranspose here: https://en.xen.wiki/w/User:Cmloegcmluin/Sandbox#null-space</ref>, and then antitransposed again at the end, or in other words, you sandwich the defactoring and HNF operations between antitransposes. | DC form is not only for mappings. Comma-bases — the duals of mappings — may also be put into DC form, as long as they are first antitransposed<ref>See a discussion of the antitranspose here: https://en.xen.wiki/w/User:Cmloegcmluin/Sandbox#null-space</ref>, and then antitransposed again at the end, or in other words, you sandwich the defactoring and HNF operations between antitransposes. | ||