View source for Isotropic quadratic form

{{TEX|done}}{{MSC|15A63}}

A [[quadratic form]] $q$ on a [[vector space]] over a field $F$ which is non-degenerate (the associated [[bilinear form]] is non-singular) but which represents zero non-trivially: there is a non-zero vector $v$ such that $q(v) = 0$.

An '''anisotropic quadratic form''' $q$ is one for which  $q(v) = 0 \Rightarrow v=0$.

====References====
* Tsit Yuen Lam, ''Introduction to Quadratic Forms over Fields'',  Graduate Studies in Mathematics '''67''',  American Mathematical Society (2005) {{ISBN|0-8218-1095-2}} {{ZBL|1068.11023}} {{MR|2104929 }} 
* J.W. Milnor, D. Husemöller, ''Symmetric bilinear forms'', Ergebnisse der Mathematik und ihrer Grenzgebiete '''73''', Springer-Verlag (1973) {{ISBN|0-387-06009-X}} {{ZBL|0292.10016}}