orthonormal basis concept
| Definition | A basis of unit vectors orthogonal to each other. Projection onto their span is the sum of the projections onto each, and a square matrix whose columns form one is an orthogonal matrix. Primer L section L.5. Also orthonormal. |
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| Example | (1, 1) over root 2 and (1, -1) over root 2 are orthonormal, each of length one and with dot product zero. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id orthonormal-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.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
none declared
Machine checked
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Used in
Data Mining as Observation primer L.
Related
basis; orthogonal; Gram and Schmidt; orthogonal matrix; projection.
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.