 | This article is rated Stub-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
| |||||||||||
This is a stub
editI have rated this article as stub and added the stub template in the article for the following points are lacking: the related notion of positive definite matrix; the matrix of a definite quadratic form and the characterization of the positiveness through the sign of the determinants of the principal minors; the important examples of the square of the Euclidean norm and of the inner product; the square root of a positive definite form is a norm; an analytic function of several real variables is convex at a point if the term of degree 2 of its Taylor expansion is a positive definite quadratic form; ;he usage of all of this in optimization. etc. D.Lazard (talk) 11:14, 21 March 2015 (UTC)
Assessment comment
editThe comment(s) below were originally left at Talk:Definite quadratic form/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
| How are your definitions of: positive definite and positive semidefinite different.
From what I read here they seem to say the same thing. I notice from the exanmple how they could mean something different, but as youve written the definition they say the same thing. (98.249.157.111 (talk) 14:11, 28 October 2009 (UTC)) |
Substituted at 18:14, 17 July 2016 (UTC)
"Negative semidefinite" listed at Redirects for discussion
edit
A discussion is taking place to address the redirect Negative semidefinite. The discussion will occur at Wikipedia:Redirects for discussion/Log/2020 June 9#Negative semidefinite until a consensus is reached, and readers of this page are welcome to contribute to the discussion. 1234qwer1234qwer4 (talk) 14:36, 9 June 2020 (UTC)
"Positive and negative definite and semidefinite and indefinite" listed at Redirects for discussion
edit A discussion is taking place to address the redirect Positive and negative definite and semidefinite and indefinite. The discussion will occur at Wikipedia:Redirects for discussion/Log/2020 June 9#Positive and negative definite and semidefinite and indefinite until a consensus is reached, and readers of this page are welcome to contribute to the discussion. 1234qwer1234qwer4 (talk) 17:42, 9 June 2020 (UTC)
Suggestion
editAn important addition to this article would be to give some criteria for the coefficient of a quadratic form that determine when a form is positive or negative definite. Theorems by Sylvester come to mind. — Preceding unsigned comment added by Zorpoid (talk • contribs) 06:44, 30 September 2023 (UTC)