triangle like \textcorner

Question

I wish to denote the algebra of all upper triangular matrices by $M_n^\textcorner(K)$ but with $\textcorner$ being a triangle. How can I create this symbol (add additional diagonal line)?

My current preamble:

\documentclass[b4paper, twoside, final, openodd, 10pt]{book}
\usepackage{etex}
\usepackage[english]{babel}
\usepackage[cp1250]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{charter}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage[framed, thmmarks]{ntheorem}
\usepackage{framed}
\usepackage{tikz}
    \usetikzlibrary{shadows,matrix,arrows}
\usepackage{hyperref}
    \hypersetup{bookmarksopen=false, pdfpagelayout=TwoPageLeft, pdflinkmargin=0pt}  %colorlinks=true, linkcolor={blue}, citecolor={green}, urlcolor={medium-blue}
\usepackage[numbered]{bookmark}
\usepackage[all]{xy}
\usepackage{mathtools}
\usepackage{animate}
\usepackage{subfigure}
\usepackage{caption}
    \captionsetup{labelformat=empty,labelsep=none}
\usepackage{verbatim}
\usepackage{multirow}
\usepackage{multicol}
\usepackage{longtable}
    \setlength{\LTpre}{0pt}\setlength{\LTpost}{0pt}
\usepackage{wrapfig}
\usepackage{cancel}
\usepackage{enumitem}
\usepackage[subfigure]{tocloft}
\usepackage[top=2.1cm, bottom=2.9cm, left=2.1cm, right=2.1cm]{geometry}
\usepackage{stmaryrd}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%        new definition of SQUARE ROOT: it renames \sqrt as \oldsqrt ()            %%
%%======http://tex.stackexchange.com/questions/29834/closed-square-root-symbol======%%
\usepackage{letltxmacro}                                                            %%
\LetLtxMacro{\oldsqrt}{\sqrt}                                                       %%
\renewcommand{\sqrt}[1][\hphantom{3}]{ \def\DHLindex{#1}\mathpalette\DHLhksqrt }    %%
\def\DHLhksqrt#1#2{ \setbox0=\hbox{$#1\oldsqrt[\DHLindex]{#2\,}$}\dimen0=\ht0       %%
                    \advance\dimen0-0.2\ht0                                         %%
                    \setbox2=\hbox{\vrule height\ht0 depth -\dimen0}                %%
                    {\box0\lower0.4pt\box2} }                                       %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                      DASHED and DOTTED UNDERLINE (ulem)                      %%
%%==============================================================================%%
\usepackage[normalem]{ulem}                                                     %%
\def\dotuline{\bgroup                                                           %%
  \ifdim\ULdepth=\maxdimen  % Set depth based on font, if not set already       %%
  \settodepth\ULdepth{(j}\advance\ULdepth.4pt\fi                                %%
  \markoverwith{\begingroup                                                     %%
  \advance\ULdepth0.08ex                                                        %%
  \lower\ULdepth\hbox{\kern.15em .\kern.1em}                                    %%
  \endgroup}\ULon}                                                              %%
%%------------------------------------------------------------------------------%%
\def\dashuline{\bgroup                                                          %%
  \ifdim\ULdepth=\maxdimen  % Set depth based on font, if not set already       %%
  \settodepth\ULdepth{(j}\advance\ULdepth.4pt\fi                                %%
  \markoverwith{\kern.15em                                                      %%
  \vtop{\kern\ULdepth \hrule width .3em}                                        %%
  \kern.15em}\ULon}                                                             %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                           CUSTOMIZED CHAPTER HEADINGS                            %%
%%==================================================================================%%
\usepackage{titlesec}   %za spreminjat chapter headinge v Article, Book, Report     %%
\usepackage{fix-cm}     %da popravi nesoglasja po redefiniranju dolžin              %%
%\titleformat{command}[shape]{format}{label}{sep}{before}[after]                    %%
\titleformat{\chapter}                                                              %%
            {\bfseries\fontsize{30pt}{25pt}\selectfont}                             %%
            {\thechapter}                                                           %%
            {8pt}                                                                   %%
            {}                                                                      %%
\titleformat{\section}                                                              %%
            {\bfseries\fontsize{22pt}{16pt}\selectfont}                             %%
            {\thesection}                                                           %%
            {5pt}                                                                   %%
            {}                                                                      %%
\titleformat{\subsection}                                                           %%
            {\fontsize{18pt}{10pt}\selectfont}                                      %%
            {\thesubsection}                                                        %%
            {4pt}                                                                   %%
            {}                                                                      %%
\titleformat{\subsubsection}                                                        %%
            {\fontsize{16pt}{10pt}\selectfont}                                      %%
            {\thesubsubsection}                                                     %%
            {4pt}                                                                   %%
            {}                                                                      %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%              CUSTOMIZED THEOREMS (ntheorem + TikZ)               %%
%-------------------------------------------------------------------%%
\theoremheaderfont{\normalfont}                                     %%
\theoremseparator{\bfseries :}                                      %%
\theorembodyfont{\normalfont\it}                                    %%
\newtheorem{envThm}{{\large\bfseries Theorem}}[section]             %%
%-------------------------------------------------------------------%%
\theoremheaderfont{\normalfont}                                     %%
\theoremseparator{\bfseries :}                                      %%
\theorembodyfont{\normalfont\it}                                    %%
\newtheorem{envPrp}[envThm]{{\large\bfseries Proposition}}          %%
%-------------------------------------------------------------------%%
\theoremheaderfont{\large}                                          %%
\theoremseparator{\bfseries :}                                      %%
\theorembodyfont{\normalfont}                                       %%
\newtheorem{envExp}[envThm]{{\large\bfseries Examples}}             %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand{\labelenumi}{\alph{enumi})}

Answer 1

I experimented a little bit with tikz library and there is a way to provide such a symbol, which scales somehow with the font size.

\documentclass{scrbook}
\usepackage{tikz}
\usepackage{xkeyval}
\usepackage{xcolor}
\usepackage{amsmath} % Not needed actually, but include if \boldmath is used
\boldmath % Not needed actually

\makeatletter
\define@key{TriSymFamily}{LineWidth}[0.05em]{%
\def\KVTriSymLineWidth{#1}}%

\define@key{TriSymFamily}{Scale}[0.01\baselineskip]{%
\def\KVTriSymScale{#1}}%


\presetkeys{TriSymFamily}{Scale=0.01\baselineskip,%    Please change at will
                           LineWidth=0.05em}{}%


\makeatother

\newcommand{\upperrighttriangle}[1][]{%
\setkeys{TriSymFamily}{#1}%
\begin{tikzpicture}[line width=\KVTriSymLineWidth,scale=\KVTriSymScale]%
%\draw (0,0) -- (1,0) -- (1,-1) -- (0,0); % 
  \draw (0,0) -- (1,0) -- (1,-1) -- cycle; %
\end{tikzpicture}%
}%

\begin{document}
% Now  your symbol in three sizes

\large
\[
{M^{\upperrighttriangle}_{n}  \left({ K} \right)} \]


\LARGE
\[
{M^{\upperrighttriangle}_{n}  \left({ K} \right)} \]

\Huge
\[
{M^{\upperrighttriangle}_{n}  \left({ K} \right)} \]

\normalsize

And now in blue colour
\textcolor{blue}{%
\[
{M^{\upperrighttriangle}_{n}  \left({ K} \right)} \]
} % End of \textcolor



\end{document}

I did not wrap your matrix symbol etc. in a special command, but it would be useful do to so, if you need that symbol at many positions.

The xkeyval version is not really necessary, it just simplifies to adapt the command to new scaling and linewidth. Another possibility would be to use pgfkeys.

EDIT I changed the drawing as suggested by Paul Gessler in a comment below, but in this case, one has to reduce the linewidth a little bit.

Here is an impression of the newer version:

And here the 'minimal' version

\documentclass{minimal}
\usepackage{tikz}

\newcommand{\upperrighttriangle}{%
\begin{tikzpicture}[line width={0.05em},scale=0.01\baselineskip]
  \draw (0,0) -- (1,0) -- (1,-1) -- cycle;%
\end{tikzpicture}%
}%


\begin{document}
\[
{M^{\upperrighttriangle}_{n}  \left({ K} \right)} \]


\end{document}

Answer 2

Here's a triangle with the pict2e package.

\documentclass{article}
\usepackage{pict2e,amsmath}

\newcommand{\utriangle}{\text{\doutriangle}}

\newcommand{\doutriangle}{%
  \linethickness{.1ex}%
  \setlength{\unitlength}{.8ex}%
  \begin{picture}(1,1)(0,-1)
  \polygon(0,1)(1,0)(1,1)
  \end{picture}%
}

\begin{document}
$M_n^{\utriangle}\quad X_{M_n^{\utriangle}}$

\bigskip

{\Large $M_n^{\utriangle}$}
\end{document}

Answer 3

This is a variant of egreg's solution, using LuaLaTeX, MetaPost and the luamplib package.

TeX dimensions are passed to MetaPost by the \mpdim command, coming directly from the gmp package (authored by egreg, by the way ;-)). It's an example of how MetaPost drawings can be tightly integrated into a LuaLaTeX program. With other engines than LuaTeX, the code can be quickly adapted from luamplib to gmp, with the drawback of needing the shell-escape functionality for a one-pass compilation.

EDIT: I've \raised the triangle less than before (.33\trianglesize instead of .66\trianglesize). It looks more esthetic as such to me. (Maybe I'm wrong in this.)

\documentclass{article}
\usepackage{amsmath,luamplib}

\newlength{\trianglesize}
\newlength{\pensize}

\newcommand{\utriangle}{%
   \text{%
      \setlength{\trianglesize}{1ex}% adapt at will
      \setlength{\pensize}{0.1ex}% adapt at will
      \begin{mplibcode}
         verbatimtex \raise .33\trianglesize etex; %box height adjustment
         beginfig(1);
         draw ((0, 1) -- (1, 0) -- (1, 1) -- cycle) scaled \mpdim{\trianglesize} 
            withpen pencircle scaled \mpdim{\pensize}; 
         endfig;
      \end{mplibcode}%
   }%
}

\begin{document}
$M_n^{\utriangle}\quad X_{M_n^{\utriangle}}$

\bigskip
{\Large $M^{\utriangle}_n$}
\end{document}