basis concept
| Definition | A 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. |
|---|---|
| Example | In the plane, e1 = (1, 0) and e2 = (0, 1) are a basis, and (3, 4) = 3 e1 + 4 e2. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id basis, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope | none |
| Prior art | none recorded |
| Evidence | none |
| Reviewed | semantic 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
none declared
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.