Commit 3afad027 authored by Jim Hefferon's avatar Jim Hefferon

edits for map2

parent 69296521
% answerjh.sty 2001-May-23
\typeout{2001-May-23 Document Style `answerjh'. Jim Hefferon}
\RequirePackage[single,nowrite]{bookans} %!!! no write !!! else ereases answers
\RequirePackage{linalgjh,bookjh}
\RequirePackage{bookjh,linalgjh}
% PAGE DIMENSIONS
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......@@ -85,7 +85,8 @@
% There is an optional argument \begin{mat}[r]{3} .. \end{mat} for
% right-flushed columns. Perhaps the rule is that numbers are better
% right-flushed but if there are any letters it is better centered?
\newenvironment{mat}[1][c]{\begin{pmatrix*}[#1]}{\end{pmatrix*}}
\newenvironment{mat}[1][c]{\begin{pmatrix*}[#1] % If mat starts with &\vdots get an error; why?
}{\end{pmatrix*}}
\newenvironment{amat}[2][c]{%
\left(\begin{array}{@{}*{#2}{#1}|#1@{}}
}{%
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......@@ -289,11 +289,13 @@ and scalar multiplication.
Thus $f_2$ is an isomorphism and we write $V\isomorphicto\polyspace_2$.
\end{example}
We are sometimes interested in an isomorphism of a space with itself,
called an \definend{automorphism}\index{automorphism}%
\index{isomorphism!of a space with itself}.
One automorphism is the identity map.
The next two examples show that there are others.
Every space is isomorphic to itself under the identity map.
\begin{definition}
An \definend{automorphism}\index{automorphism}%
is an isomorphism of a space with
itself\index{isomorphism!of a space with itself}.
\end{definition}
\begin{example} \label{exam:RigidPlaneMapsAutos}
A \definend{dilation}\index{dilation}\index{automorphism!dilation}
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