Non-negative Quadratic forms with Exterior Forms - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T15:15:01Z http://mathoverflow.net/feeds/question/120762 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/120762/non-negative-quadratic-forms-with-exterior-forms Non-negative Quadratic forms with Exterior Forms Munmoon Salehi 2013-02-04T11:59:46Z 2013-02-12T08:44:08Z <p>Hello All, </p> <p>I apologize if the following question is too elementary. Any suggestion is greatly appreciated. Thank you.</p> <p>Let $n\geqslant 4$, $X$ be an $n$-dimensional inner product space over $\mathbb{R}$ and let $T:\Lambda^{2}(X)\rightarrow \Lambda^{2}(X)$ be a symmetric linear operator satisfying $$\langle T(\omega),\omega\rangle\geqslant 0,\text{ for all }\omega\in \Lambda^{2}(X)\text{ with }\omega\wedge\omega=0.$$ Is it true that, for some $A\in \Lambda^{4}(X)$, $$\langle T(\omega),\omega\rangle\geqslant 0,\text{ for all }\omega\in \Lambda^{2}(X)\text{ with }\langle A;\omega\wedge\omega\rangle=0?$$</p>