amsmathmath-mode
I m trying this
T(n) \epsilon \left(\Theta(n^\log_22$\right) = $\Theta(n^\log_22 )$ = $\Theta(n)$
but i want below result. Is E sign is epsilon only . And also log bracket not coming properly and space before aND AFTER EPSILON NOT CORRECT.
Generally online it is given as
\[
$A(n) \in \Theta(n^{\log_b a}) = \Theta(n^{\log_2 2} ) = \Theta(n)$
\]
so i am asking what these \[ and \] brackets do.
I think, the problem is rather that the minus sign has a large width, larger than the digits. Because of this the minus sign becomes more weight in centered alignments.
The following example only uses the digit width of the minus sign for the aligment and reduces the total width of the minus sign to 110% of the digit width. Usually there is enough white space at the left of the number thus that the protruding does not hurt to much.
\documentclass[11pt,a4paper]{article}
\usepackage{amsmath}
\usepackage{mathtools}
\usepackage{graphicx}
\newcommand*{\matminus}{%
\leavevmode
\hphantom{0}%
\llap{%
\settowidth{\dimen0 }{$0$}%
\resizebox{1.1\dimen0 }{\height}{$-$}%
}%
}
\begin{document}
\[
A = \begin{pmatrix*}
\matminus1 & \matminus10 & 1 \\
100 & 5 & 16 \\
13 & 7 & 7
\end{pmatrix*}.
\]
\end{document}
The suggestion above is a compromise between different requirements. Of course, also the numbers can also be centered without taking into account the minus sign without changing the column margins. But then the cell entries are not independent any more, the typesetting depends on the values in the other rows:
\llap{$-$} sets the minus sign and lets TeX think, the width is zero. That matches the centering requirement. But depending on the other values in the other rows, additional
white space needs to be inserted at the left of the column.\hphantom{-} does not set a minus sign, but only the horizontal space. It can help for the proper alignment of positive and negative numbers, but there might be the need to reduce the white space at the left side of the column depending on the other values in the column.There is a bunch of options to improve this:
= is better\left(....\right) to get bigger bracket, however the spacing before and after brackets are too large\biggl(...\biggr) for larger brackets and better spacing\mleft( and \mright) from the mleftright package for adapted brackets and better spacingThe output of those options can be seen from the screen shot
\documentclass{article}
\usepackage{fancyhdr} % Required for custom headers
\usepackage{lastpage} % Required to determine the last page for the footer
\usepackage{extramarks} % Required for headers and footers
\usepackage[usenames,dvipsnames]{color} % Required for custom colors
\usepackage{graphicx} % Required to insert images
\usepackage{listings} % Required for insertion of code
\usepackage{courier} % Required for the courier font
\usepackage{lipsum} % Used for inserting dummy 'Lorem ipsum' text into the template
\usepackage{mathtools} %loads amsmath as well
\usepackage{mleftright}
\DeclarePairedDelimiter\Floor\lfloor\rfloor
\DeclarePairedDelimiter\Ceil\lceil\rceil
% Margins
\topmargin=-0.45in
\evensidemargin=0in
\oddsidemargin=0in
\textwidth=6.5in
\textheight=9.0in
\headsep=0.25in
\linespread{1.1} % Line spacing
\begin{document}
\section{eqn}
\begin{itemize}
\item original \\
T(n)= $\sum\limits_{i=3}^{n-4}(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1)$
\item Now with extra space
$ T(n)\;= \sum\limits_{i=3}^{n-4}(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1)$
\item With brackets improved
$T(n)\;= \sum\limits_{i=3}^{n-4}\left(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1\right)$
\item With big brackets \texttt{biggl(} and \texttt{biggr)}
$T(n) = \sum\limits_{i=3}^{n-4}\biggl(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1\biggr)$
\item With brackets from mleftright package
$ T(n)= \sum\limits_{i=3}^{n-4}\mleft(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1\mright)$
\item Displaystyle all together
\[ T(n)\;= \sum\limits_{i=3}^{n-4}\mleft(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1\mright) \]
\end{itemize}
Now in an align-environment
\begin{align}
T(n)&= \sum\limits_{i=3}^{n-4}(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1) \\
T(n)&= \sum\limits_{i=3}^{n-4}\left(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1\right) \\
T(n)&= \sum\limits_{i=3}^{n-4}\mleft(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1\mright)
\end{align}
\end{document}
Best Answer
Don't use
\epsilonfor "element of"; instead, use the\inmacro.You need to place curly braces around the material that's to be placed in the exponent positions.
Don't switch in and out of math mode in one and the same equation.