Basis: Difference between revisions
Cmloegcmluin (talk | contribs) m add pronunciation information for plural back |
Cmloegcmluin (talk | contribs) m full-grade doesn't make sense; should have been full-rank |
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The verb used for the process by which linear combinations of the basis vectors reach all of the subspace vectors is "spanning"; we say that the basis vectors '''span''' the subspace. | The verb used for the process by which linear combinations of the basis vectors reach all of the subspace vectors is "spanning"; we say that the basis vectors '''span''' the subspace. | ||
Importantly, a set of vectors that spans a subspace but is not [[full-rank | Importantly, a set of vectors that spans a subspace but is not [[full-rank]], that is, includes [[linear dependence|linearly dependent]] vectors, or in less technical terms "redundant" vectors, is not considered a basis; in that case, it is merely a spanning set. | ||
=== Relationship to groups === | === Relationship to groups === | ||