From c5f63d5c2c6d10d6566a83dec23f31252319a55f Mon Sep 17 00:00:00 2001 From: James Geddes Date: Tue, 16 Apr 2024 16:56:50 +0100 Subject: [PATCH] Quadratic forms --- notes/mml.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/notes/mml.tex b/notes/mml.tex index 33710c5..425905e 100644 --- a/notes/mml.tex +++ b/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.