\documentclass{article} \usepackage{amssymb} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %TCIDATA{OutputFilter=LATEX.DLL} %TCIDATA{Created=Monday, June 25, 2001 17:45:57} %TCIDATA{LastRevised=Monday, March 24, 2003 13:27:45} %TCIDATA{} %TCIDATA{} %TCIDATA{CSTFile=On line bluem.cst} %TCIDATA{PageSetup=72,72,72,72,0} %TCIDATA{AllPages= %H=36 %F=36,\PARA{038
\QTR{small}{Matematick\U{e1} anal\U{fd}za II online - D\U{f4}kazy\dotfill \thepage }} %} \newtheorem{theorem}{Theorem} \newtheorem{acknowledgement}[theorem]{Acknowledgement} \newtheorem{algorithm}[theorem]{Algorithm} \newtheorem{axiom}[theorem]{Axiom} \newtheorem{case}[theorem]{Case} \newtheorem{claim}[theorem]{Claim} \newtheorem{conclusion}[theorem]{Conclusion} \newtheorem{condition}[theorem]{Condition} \newtheorem{conjecture}[theorem]{Conjecture} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{criterion}[theorem]{Criterion} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{exercise}[theorem]{Exercise} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{notation}[theorem]{Notation} \newtheorem{problem}[theorem]{Problem} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{remark}[theorem]{Remark} \newtheorem{solution}[theorem]{Solution} \newtheorem{summary}[theorem]{Summary} \newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}} \input{tcilatex} \begin{document} \author{A. U. Thor} \title{Lab Report} \date{The Date } \maketitle \begin{abstract} A Laboratory report created with Scientific Notebook \end{abstract} \section{Taylorova veta} \subsection{Veta o odhade kladne definitnej kvadratickej formy.} \textbf{D\^{o}kaz: }Preto\v{z}e $q(\mathbf{h})$ je kone\v{c}n\'{a} suma s% \'{u}\v{c}inov komponent $\mathbf{h}$ a prvkov matice, je spojit\'{a} na $% \mathbf{R}^{n}.$ Nech \[ m=\min_{\mathbf{h}\in S}q(\mathbf{h}) \]% je minimum na mno\v{z}ine $S=\{\mathbf{h}\in \mathbf{R}^{n};\,\left\| \mathbf{h}\right\| =1\}.$ $m>0,$ preto\v{z}e minimum sa na kompaktnej mno% \v{z}ine $S$ nadob\'{u}da v nejakom bode z $S.$ Potom pre ka\v{z}d\'{e} $% \mathbf{h}\in \mathbf{R}^{n},\,\mathbf{h}$ $\neq $ $\mathbf{0}$ je $\frac{% \mathbf{h}}{\left\| \mathbf{h}\right\| }\in S$ a tak plat\'{\i} \[ q\left( \frac{\mathbf{h}}{\left\| \mathbf{h}\right\| }\right) =\frac{1}{% \left\| \mathbf{h}\right\| }q(\mathbf{h})\geq m.\blacksquare \] \begin{center} \begin{tabular}{|c|} \hline {\small \hyperref{Sp\"{a}\v{t}}{}{}{Ma42.tex#5}} \\ \hline \end{tabular} \end{center} \rule{6.5in}{0.04in} \textsl{Matematick\'{a} anal\'{y}za II} \end{document}