# Isotropic quadratic form

From Encyclopedia of Mathematics

2020 Mathematics Subject Classification: *Primary:* 15A63 [MSN][ZBL]

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 MR2104929 - 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

**How to Cite This Entry:**

Isotropic quadratic form.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Isotropic_quadratic_form&oldid=54477