Abstract
A quadratic form q on E is a map of the form
where P is a symmetric bilinear form over E; such a P is well determined by q by the formula
and is called the polar form of q. Over a subspace F of E, the restriction of q is still a quadratic form, denoted by q| F .
Here E is a vector space of finite dimension n over a commutative field of characteristic different from 2.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1984 Marcel Berger
About this chapter
Cite this chapter
Berger, M., Pansu, P., Berry, JP., Saint-Raymond, X. (1984). Quadratic Forms. In: Problems in Geometry. Problem Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1836-2_13
Download citation
DOI: https://doi.org/10.1007/978-1-4757-1836-2_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2822-1
Online ISBN: 978-1-4757-1836-2
eBook Packages: Springer Book Archive