Basis: Difference between revisions
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{{Wikipedia| Basis (linear algebra) }} | {{Wikipedia| Basis (linear algebra) }} | ||
A '''basis''' is a list of vectors that represents the infinite set of vectors that are combinations of them. The corresponding infinite set is called its '''subspace''' | A '''basis''' (plural ''bases'') is a list of vectors that represents the infinite set of vectors that are combinations of them. The corresponding infinite set is called its '''subspace'''. | ||
Bases are mathematical structures that come from the field of [[Wikipedia:Linear algebra|linear algebra]], and are used in [[regular temperament theory]], where the most common example of a basis is a [[comma basis]]. The fact that a comma basis is a ''basis'' conveys how when a temperament makes the set of commas explicitly listed in a comma basis [[vanish]], then it also makes any interval that's equal to any combination of those commas vanish. We could never possibly list the infinitude of commas made to vanish in this way, so instead we carefully choose a minimal set of commas that is capable of representing all of them. | Bases are mathematical structures that come from the field of [[Wikipedia:Linear algebra|linear algebra]], and are used in [[regular temperament theory]], where the most common example of a basis is a [[comma basis]]. The fact that a comma basis is a ''basis'' conveys how when a temperament makes the set of commas explicitly listed in a comma basis [[vanish]], then it also makes any interval that's equal to any combination of those commas vanish. We could never possibly list the infinitude of commas made to vanish in this way, so instead we carefully choose a minimal set of commas that is capable of representing all of them. | ||