Singular quadratic space - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T02:27:54Z http://mathoverflow.net/feeds/question/101149 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/101149/singular-quadratic-space Singular quadratic space Wanderer 2012-07-02T14:33:53Z 2012-07-02T14:33:53Z <p>Let $(V,b)$ a symmetric bilinear space. An old theorem of Witt says that if $(V,b)$ is regular, then given a subspace $W$ of $V$ and an isometry $\sigma: W \to V$, there exists an isometry $\Sigma: V \to V$ which extends $\sigma$.</p> <p>Does this necessarily fail if $(V,b)$ is singular - e.g. if the radical $V^\perp$ is one-dimensional?</p>