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basis concept

DefinitionA set of independent vectors whose span is the whole space, so that every vector is exactly one combination of them. The standard basis vectors have a one in one coordinate and zeros elsewhere. Primer L section L.1.
ExampleIn the plane, e1 = (1, 0) and e2 = (0, 1) are a basis, and (3, 4) = 3 e1 + 4 e2.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id basis, kind concept.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equationnone
Assumptions and scopenone
Prior artnone recorded
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Reviewedsemantic review 2026-09-09; generated 2026-09-10 from records at the commits on the provenance page.

Equation

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Conditions

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Ledger

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First stated

Primer L section L.1 of Data Mining as Observation, added in draft 0.3 (2026-09-09) for the ECE 514 readers whose first courses are far behind. The idea is standard and TSK Appendix A covers it at length.

Measurements

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Failures and corrections

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Invariance envelope

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Machine checked

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Used in

Data Mining as Observation primer L, chapters 0, 11.

Related

span; linear independence; orthonormal basis; vector.

See also

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Status

Generated 2026-09-10 by encyclopedia/generate.py; book at observation-data-mining f3914f0; the commit of every record is listed in the encyclopedia’s provenance.

← base rateBayes' rule →