NonDegenerateBilinearForm 2002-02-22 03:36:12 2005-05-10 05:16:53 Definition % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here A bilinear form $B$ over a vector space $V$ is said to be {\em non-degenerate} when \begin{itemize} \item if $B({{\bf x}},{{\bf y}}) = 0$ for all ${{\bf x}} \in V$, then ${{\bf y}} = {{\bf 0}}$, and \item if $B({{\bf x}},{{\bf y}}) = 0$ for all ${{\bf y}} \in V$, then ${{\bf x}} = {{\bf 0}}$. \end{itemize}