Quadratic forms

notes/mml.tex

@@ -181,10 +181,10 @@ \section*{Introduction}
 \section{Quadratic forms on vector spaces}
 
 Let $V$ be a (finite-dimensional) real vector space. Recall that the
-\emph{dual} of $V$, written $V*$, is the vector space of all linear
+\emph{dual} of $V$, written $V^*$, is the vector space of all linear
 maps from $V$ to~$R$. 
 
-Suppose $T\colon V\toV^*$ is a linear map. For any $u, v\in V$, $T(v)$
+Suppose $T\colon V\to V^*$ is a linear map. For any $u, v\in V$, $T(v)$
 is a an element of $V^*$, and thus $[T(v)](u)$ is a number. By abuse
 of notation, we write this as $T(v,u)$. Thus we can think of $T$ as a
 (multi-)linear map from pairs of vectors in $V$ to the reals.