Copositive and completely positive quadratic forms
- 1 April 1963
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 59 (2), 329-339
- https://doi.org/10.1017/s0305004100036951
Abstract
A copositive quadratic form is a real form which is non-negative for non-negative arguments. A completely positive quadratic form is a real form which can be written as a sum of squares of non-negative real forms. The completely positive forms are basic in the study of block designs arising in combinatorial analysis (3). The copositive forms arise in the theory of inequalities and have been considered in a paper by Mordell (4) and two papers by Diananda(1, 2).Keywords
This publication has 3 references indexed in Scilit:
- On non-negative forms in real variables some or all of which are non-negativeMathematical Proceedings of the Cambridge Philosophical Society, 1962
- On a Conjecture of L. J. Mordell Regarding an Inequality Involving Quadratic FormsJournal of the London Mathematical Society, 1961
- On the inequality $$\sum\limits_{r = 1} {x_r /(x_{r + 1} + x_{r + 2} ) \geqslant n/2} $$ and some othersand some othersAbhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 1958