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positive definite concept

DefinitionA symmetric matrix whose quadratic form is positive for every nonzero vector, which is the same as every eigenvalue being positive. Positive semidefinite allows zero. Primer L section L.6.
ExampleRows (2, 1) and (1, 2) have eigenvalues 3 and 1 and are positive definite, while rows (1, 2) and (2, 1) give -2 at (1, -1) and are not.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id positive-definite, kind concept.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equationnone
Assumptions and scopenone
Prior artnone recorded
Evidencenone
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.6 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

positive semidefinite; quadratic form; eigenvalue, eigenvector.

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.

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