diff --git a/documents/math-sylvester-diagonal-matrix/Makefile b/documents/math-sylvester-diagonal-matrix/Makefile index a4ff038..07f017c 100644 --- a/documents/math-sylvester-diagonal-matrix/Makefile +++ b/documents/math-sylvester-diagonal-matrix/Makefile @@ -4,6 +4,7 @@ DENSITY = 300 WIDTH = 500 make: + pdflatex $(SOURCE).tex -output-format=pdf pdflatex $(SOURCE).tex -output-format=pdf make clean diff --git a/documents/math-sylvester-diagonal-matrix/math-sylvester-diagonal-matrix.tex b/documents/math-sylvester-diagonal-matrix/math-sylvester-diagonal-matrix.tex index 97f6b3b..f97378a 100644 --- a/documents/math-sylvester-diagonal-matrix/math-sylvester-diagonal-matrix.tex +++ b/documents/math-sylvester-diagonal-matrix/math-sylvester-diagonal-matrix.tex @@ -3,39 +3,43 @@ \setlength\PreviewBorder{0mm} \usepackage{amsmath,array} -\renewcommand\arraycolsep{4pt} % default value: 6pt +\usepackage{tikz} +\usetikzlibrary{decorations.pathreplacing} + +\setlength\arraycolsep{4pt} % default value: 6pt + +\newcommand\tikzmark[1]{% + \tikz[overlay,remember picture,baseline] \coordinate [anchor=base] (#1);} + +\newcommand\DrawBrace[3]{% + \draw [decorate,decoration={brace,amplitude=2pt,mirror,raise=2pt}] + (#1) -- (#2) node [black,midway,sloped,yshift=-10pt] {\footnotesize$#3$}; +} \begin{document} \begin{preview} \begin{equation*} -S^T \cdot A \cdot S = -\left( \, -\begin{array}{r@{}r@{}r r r} % @{} is used twice to suppress intercolumn whitespace - \underbrace{ - \begin{array}{rrr} % First block (1) - 1 & & \\ - & \ddots & \\ - & & 1 \\ - \end{array} - }_{r_+(s)-mal}\\ - & - \underbrace{ - \begin{array}{rrr} % Second block (-1) - -1 & & \\ - & \ddots & \\ - & & -1\\ - \end{array} - }_{r_{-}(s)-mal} \\ - & & - \underbrace{ - \begin{array}{rrr} % Third block - 0 & & \\ - & \ddots & \\ - & & 0\\ - \end{array} - }_{r_0(s)-mal} \\ -\end{array}\,\right) +S^T \cdot A \cdot S = +\left( +\begin{array}{*{9}{c}} +\tikzmark{a}1 \\ +& \ddots & \\ +& & \tikzmark{b}1 \\ +& & & \tikzmark{c}-1 \\ +& & & & \ddots & \\ +& & & & & \tikzmark{d}-1\\ +& & & & & & \tikzmark{e}\phantom{-}0 \\ +& & & & & & & \ddots & \\ +& & & & & & & & \tikzmark{f}\phantom{-}0 \\ +\end{array} +\right) \end{equation*} + +\begin{tikzpicture}[remember picture,overlay] +\DrawBrace{a}{b}{r_{+}(s)-mal} +\DrawBrace{c}{d}{r_{-}(s)-mal} +\DrawBrace{e}{f}{r_{0}(s)-mal} +\end{tikzpicture} \end{preview} \end{document}