Basis: Difference between revisions
m Plural needn't a separate paragraph |
→Mathematical details: this information wasn't accurate -- basis is used in vector spaces as well as free abelian groups, which models ji |
||
| Line 24: | Line 24: | ||
=== Relationship to groups === | === Relationship to groups === | ||
The basis is a concept used across vector spaces and [[Wikipedia: Free abelian group|free abelian groups]]. The analogous concept for [[Wikipedia: Group (mathematics)|groups]] and [[Wikipedia: Module (mathematics)|modules]] in general, which are structures within the broader field of [[Wikipedia: Abstract algebra|abstract algebra]], is known as the [[Wikipedia: Generating set of a module|minimal generating set]]. | |||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ Comparison of terms in linear algebra and group theory | ||
|- | |||
! "Within a {}, …" | ! "Within a {}, …" | ||
! "…a {}…" | ! "…a {}…" | ||
| Line 49: | Line 49: | ||
The sense of "subgroup" in this table is different than [[Just_intonation_subgroup|the specialized meaning it has taken on in RTT]]. Also, the sense of "generator" in this table is different than the one used for [[MOS scale]]s in the context of [[period]]s; for further disambiguating information, see [[generator]]. | The sense of "subgroup" in this table is different than [[Just_intonation_subgroup|the specialized meaning it has taken on in RTT]]. Also, the sense of "generator" in this table is different than the one used for [[MOS scale]]s in the context of [[period]]s; for further disambiguating information, see [[generator]]. | ||
== Basis vs subspace == | == Basis vs subspace == | ||