Gram and Schmidt concept
| Definition | The procedure that turns independent vectors into an orthonormal basis for their span, dividing the first by its length and subtracting from each next vector its projections onto the basis made so far. Primer L section L.5. Also Gram-Schmidt. |
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| Example | From (3, 4) and (1, 0), the first basis vector is (0.6, 0.8), then (1, 0) - 0.6 (0.6, 0.8) = (0.64, -0.48), so the second is (0.8, -0.6). |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id gram-schmidt, 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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Ledger
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First stated
Primer L section L.5 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.
Related
orthonormal basis; projection; residual.
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.