4

I am typing these inequalities with the label as follows

\begin{equation}\label{(4.51)}
\begin{matrix}
\la g(x_m(\tau_m(t)),u_m(\tau_m(t)) ) -g(x^{i+1}_m,u^{i+1}_m), y^n_m(t)- x_m(\tau_m(t))\ra &\leq & L' \|x_m(\tau_m(t))-x^{i+1}_m \| \| y^n_m(t)-x_m(\tau_m(t)) \| \\
&\leq & L' K \frac{T}{m} \| y^n_m(t)-x_m(\tau_m(t))\| \\
&\leq & L' 3K^2 \frac{T}{m} \\
&\leq &\frac{C_3}{m},
\end{matrix}
\end{equation}

How can I make the distance between these rows is bigger? Thank you so much for your help.

Norman Gray
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Ross
  • 175
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3 Answers3

3

In general, in display constructions the end of line marker \\ takes an optional argument specifying extra vertical space that may be added. So you can write 

\\[1ex]

instead of just \\ to get one ex of extra space. Adding this to your code for each line removes the crampedness. However, you are using the wrong environment for a multiline display. matrix is for ordinary matrices with equally spaced entries. You should be using environments from the amsmath package or the superset mathtools. In this case a split inside an equation is most appropriate.

The document below contains four equations. The first with roughly your original coding, very cramped. The second with your coding with \\[1ex] added, this is better vertical spacing but the mathematics is still typeset in a too compact style on each line, and placement of the inequality signs is not good. The third gives a standard split inside equation and I have used mathtools' command \MoveEqLeft to get good positioning of the first line. The final equation is the equation+split with extra vertical spacing, which should not really be necessary any more.

Sample output

\documentclass{article}

\usepackage{mathtools}

\begin{document}
\begin{equation}\label{(4.51)}
\begin{matrix}
&&\langle g(x_m(\tau_m(t)),u_m(\tau_m(t)) ) -g(x^{i+1}_m,u^{i+1}_m),
y^n_m(t)- x_m(\tau_m(t))\rangle \\
&\leq & L' \|x_m(\tau_m(t))-x^{i+1}_m \| \| y^n_m(t)-x_m(\tau_m(t)) \| \\
&\leq & L' K \frac{T}{m} \| y^n_m(t)-x_m(\tau_m(t))\| \\
&\leq & L' 3K^2 \frac{T}{m} \\
&\leq &\frac{C_3}{m},
\end{matrix}
\end{equation}

\begin{equation}\label{eq:orig-spaced}
\begin{matrix}
&&\langle g(x_m(\tau_m(t)),u_m(\tau_m(t)) ) -g(x^{i+1}_m,u^{i+1}_m),
y^n_m(t)- x_m(\tau_m(t))\rangle \\[1ex]
&\leq & L' \|x_m(\tau_m(t))-x^{i+1}_m \| \| y^n_m(t)-x_m(\tau_m(t)) \| \\[1ex]
&\leq & L' K \frac{T}{m} \| y^n_m(t)-x_m(\tau_m(t))\| \\[1ex]
&\leq & L' 3K^2 \frac{T}{m} \\[1ex]
&\leq &\frac{C_3}{m},
\end{matrix}
\end{equation}

\begin{equation}\label{eq:split}
  \begin{split}
    \MoveEqLeft
    \langle g(x_m(\tau_m(t)),u_m(\tau_m(t)) ) -g(x^{i+1}_m,u^{i+1}_m),
    y^n_m(t)- x_m(\tau_m(t))\rangle \\
    &\leq  L' \|x_m(\tau_m(t))-x^{i+1}_m \| \| y^n_m(t)-x_m(\tau_m(t)) \| \\
    &\leq  L' K \frac{T}{m} \| y^n_m(t)-x_m(\tau_m(t))\| \\
    &\leq  L' 3K^2 \frac{T}{m} \\
    &\leq \frac{C_3}{m},
  \end{split}
\end{equation}

\begin{equation}\label{eq:space}
  \begin{split}
    \MoveEqLeft
    \langle g(x_m(\tau_m(t)),u_m(\tau_m(t)) ) -g(x^{i+1}_m,u^{i+1}_m),
    y^n_m(t)- x_m(\tau_m(t))\rangle \\[1ex]
    &\leq  L' \|x_m(\tau_m(t))-x^{i+1}_m \| \| y^n_m(t)-x_m(\tau_m(t)) \| \\[1ex]
    &\leq  L' K \frac{T}{m} \| y^n_m(t)-x_m(\tau_m(t))\| \\[1ex]
    &\leq  L' 3K^2 \frac{T}{m} \\
    &\leq \frac{C_3}{m},
  \end{split}
\end{equation}

\end{document}
Andrew Swann
  • 95,762
2

I am guessing that this is what you might be looking for

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}
\begin{document}
\begin{align}
\MoveEqLeft\left( g(x_m(\tau_m(t)),u_m(\tau_m(t)) ) -g(x^{i+1}_m,u^{i+1}_m), y^n_m(t)-
x_m(\tau_m(t))\right) \notag\\
&~\leq~  L' \|x_m(\tau_m(t))-x^{i+1}_m \| \| y^n_m(t)-x_m(\tau_m(t)) \| \notag\\
&~\leq~ L' K \frac{T}{m} \| y^n_m(t)-x_m(\tau_m(t))\| \notag\\
&~\leq~ L' 3K^2 \frac{T}{m} \notag\\
&~\leq~\frac{C_3}{m}\;,\label{(4.51)}
\end{align}
\end{document}

enter image description here

I replace \la and \ra by what I guessed they might stand for. You should not use matrix if you are typing equations. Notice that this is a so-called minimal working example, i.e. a compilable code, which you are always supposed to provide in questions.

  • 2
    That's the way to do it, except for the ~ signs you put in there. They make the spacing around the inequalities too large, just like bad old eqalign (see this ancient answer). – Harald Hanche-Olsen Nov 29 '17 at 06:52
  • @HaraldHanche-Olsen Sorry, the ~ signs are there for a reason. I am aware of some people not liking them, but I really prefer readable equations. Note that the old eqnarray environment had similar spacings, but this environment is now deprecated. –  Nov 29 '17 at 13:01
1

Here's a solution that uses an aligned environment inside an equation environment.

enter image description here

\documentclass{article}
\usepackage{mathtools}
\DeclarePairedDelimiter\norm\lVert\rVert
\begin{document}
\begin{equation}\label{(4.51)}
\begin{aligned}[b]
&\bigl\langle g(x_m(\tau_m(t)),u_m(\tau_m(t)) ) -g(x^{i+1}_m,u^{i+1}_m), y^n_m(t)- x_m(\tau_m(t))\bigr\rangle \\
&\qquad\leq L' \norm[\big]{x_m(\tau_m(t))-x^{i+1}_m} \norm[\big]{ y^n_m(t)-x_m(\tau_m(t))} \\
&\qquad\leq L' K \frac{T}{m} \norm[\big]{y^n_m(t)-x_m(\tau_m(t))} \\
&\qquad\leq L' 3K^2 \frac{T}{m} \\
&\qquad\leq \frac{C_3}{m}\,.
\end{aligned}
\end{equation}
\end{document}
Mico
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