Positive definiteness
title: "Positive definiteness" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["quadratic-forms"] topic_path: "general/quadratic-forms" source: "https://en.wikipedia.org/wiki/Positive_definiteness" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
In mathematics, positive definiteness is a property of any object to which a bilinear form or a sesquilinear form may be naturally associated, which is positive-definite. See, in particular:
- Positive-definite bilinear form
- Positive-definite function
- Positive-definite function on a group
- Positive-definite functional
- Positive-definite kernel
- Positive-definite matrix
- Positive-definite operator
- Positive-definite quadratic form
References
- {{citation | last = Fasshauer | first = Gregory E. | journal = Dolomites Research Notes on Approximation | pages = 21–63 | title = Positive definite kernels: Past, present and future | url = http://www.math.iit.edu/~fass/PDKernels.pdf | volume = 4 | year = 2011}}.
- {{citation | last = Stewart | first = James | doi = 10.1216/RMJ-1976-6-3-409 | issue = 3 | journal = The Rocky Mountain Journal of Mathematics | mr = 0430674 | pages = 409–434 | title = Positive definite functions and generalizations, an historical survey | volume = 6 | year = 1976| doi-access = free
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