Basis: Difference between revisions
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Cmloegcmluin (talk | contribs) →Basis vs subspace: note about non-uniqueness and canonical form |
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And when we ''are'' referring to the basis itself, it's perfectly fine to refer to a "subspace basis" as a "basis" for short, as we have been doing throughout this article, because there's no other type of basis in this context; something being a "basis" here implies that it is a "subspace basis". | And when we ''are'' referring to the basis itself, it's perfectly fine to refer to a "subspace basis" as a "basis" for short, as we have been doing throughout this article, because there's no other type of basis in this context; something being a "basis" here implies that it is a "subspace basis". | ||
We do have to be careful, though, to remember that a subspace has infinitely many possible basis representations. This is why [[canonical form]]s are typically developed for them, as they have been for mappings and comma bases, so that each subspace ''does'' have a uniquely identifying basis. | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Terms]] | [[Category:Terms]] | ||
[[Category:Math]] | [[Category:Math]] | ||