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'matrix representation'
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| Title of object: |
matrix representation |
| Canonical Name: |
MatrixRepresentation |
| Type: |
Definition |
| Created on: |
2004-12-14 20:34:26 |
| Modified on: |
2004-12-14 20:43:54 |
| Classification: |
msc:20C99 |
Preamble:
\usepackage{graphicx}
%\usepackage{xypic}
\usepackage{bbm}
\newcommand{\Z}{\mathbbmss{Z}}
\newcommand{\C}{\mathbbmss{C}}
\newcommand{\R}{\mathbbmss{R}}
\newcommand{\Q}{\mathbbmss{Q}}
\newcommand{\mathbb}[1]{\mathbbmss{#1}}
\newcommand{\figura}[1]{\begin{center}\includegraphics{#1}\end{center}}
\newcommand{\figuraex}[2]{\begin{center}\includegraphics[#2]{#1}\end{center}}
\newtheorem{dfn}{Definition} |
Content:
A matrix representation of a group $G$ is a group homomorphism between $G$ and $GL_n(\C)$, that is, a function
\[ X:G\to GL_n(\C)\]
such that
\begin{itemize}
\item $X(gh)=X(g)X(h)$,
\item $X(e)=I$
\end{itemize}
Notice that this definition is equivalent to the group representation definition when the vector space $V$ is finite dimensional over $\C$. |
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