+\begin_layout Standard
+Sum (
+\begin_inset Formula $\sum$
+\end_inset
+
+) and integral (
+\begin_inset Formula $\int$
+\end_inset
+
+) operators are very often decorated with limits.
+ These limits can be entered in \SpecialChar LyX
+ by entering them as you would enter a super-
+ or subscript, directly after the symbol.
+ The sum operator will automatically place its
+\begin_inset Quotes eld
+\end_inset
+
+limits
+\begin_inset Quotes erd
+\end_inset
+
+ over and under the symbol in displayed formulas, and to the side in inline
+ formulas, as in
+\begin_inset Formula $\sum_{n=0}^{\infty}\frac{1}{n!}=e$
+\end_inset
+
+, versus
+\begin_inset Formula
+\[
+\sum\nolimits _{n=0}^{\infty}\frac{1}{n!}=e
+\]
+
+\end_inset
+
+Integral signs, however, will place the limits to the side in both formula
+ types.
+\end_layout
+
+\begin_layout Standard
+All operators with limits will be automatically re-sized when placed in
+ display mode.
+ The placement of the limits can be changed by placing the cursor directly
+ behind the operator and using the menu
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Change
+\begin_inset space ~
+\end_inset
+
+Limits
+\begin_inset space ~
+\end_inset
+
+Type
+\family default
+ or entering
+\begin_inset Info
+type "shortcut"
+arg "math-limits"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Certain other mathematical expressions also have this
+\begin_inset Quotes eld
+\end_inset
+
+moving limits
+\begin_inset Quotes erd
+\end_inset
+
+ feature, such as
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Limits
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula
+\[
+\lim_{x\rightarrow\infty}f(x),
+\]
+
+\end_inset
+
+which will place the
+\begin_inset Formula $x\rightarrow\infty$
+\end_inset
+
+ underneath the
+\begin_inset Quotes eld
+\end_inset
+
+lim
+\begin_inset Quotes erd
+\end_inset
+
+ in display mode.
+ In inline formulas it looks like this:
+\begin_inset Formula $\lim_{x\rightarrow\infty}f(x)$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Note that the lim-function was entered as the function macro
+\series bold
+
+\backslash
+lim
+\series default
+.
+ Have a look at section
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Functions"
+
+\end_inset
+
+ for an explanation of function macros.
+\end_layout
+
+\begin_layout Subsection
+Math Symbols
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Symbols
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Most math symbols can be found in the
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Panel
+\family default
+ under one of several categories; including
+\family sans
+Greek
+\family default
+,
+\family sans
+Operators
+\family default
+,
+\family sans
+Relations
+\family default
+,
+\family sans
+Arrows
+\family default
+.
+ There are also the additional symbols provided by the American Mathematical
+ Society (AMS).
+\end_layout
+
+\begin_layout Standard
+If you know the \SpecialChar LaTeX
+-command for a construct or symbol you wish to use, you
+ don't have to use the
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Panel
+\family default
+; you can type the command directly into the formula.
+ \SpecialChar LyX
+ will convert it to the corresponding symbol or construct.
+\end_layout
+
+\begin_layout Subsection
+Altering Spacing
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Spaces
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You may want to create spaces that differ from the standard spacing that
+ \SpecialChar LaTeX
+ provides.
+ To do this, press
+\begin_inset Info
+type "shortcut"
+arg "command-alternatives math-space ; space-insert protected"
+\end_inset
+
+ or use the
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Panel
+\family default
+ button
+\begin_inset Info
+type "icon"
+arg "math-insert \\space"
+\end_inset
+
+.
+ This generates a small space, and shows a small marker on the screen.
+ For example, the sequence
+\series bold
+a Ctrl+Space b
+\series default
+:
+\begin_inset Formula $a\,b$
+\end_inset
+
+ appears in \SpecialChar LyX
+ as
+\begin_inset Graphics
+ filename clipart/SpaceMarker.png
+
+\end_inset
+
+.
+ You can change the space to different sizes when you set the cursor behind
+ the space marker and enter space again several times.
+ With every space enter the size will be changed.
+ Some markers for the space size appear red in \SpecialChar LyX
+, because they are negative
+ spaces.
+ Here are two examples:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+a Ctrl+Space b
+\series default
+ and 3×
+\family sans
+Space
+\family default
+:
+\begin_inset Formula $a\quad b$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+a Ctrl+Space b
+\series default
+ and 5×
+\family sans
+Space
+\family default
+:
+\begin_inset Formula $a\!b$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Functions
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Functions
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Functions"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Panel
+\family default
+ contains under the button
+\begin_inset Info
+type "icon"
+arg "math-insert \\functions"
+\end_inset
+
+ a number of function macros, such as
+\begin_inset Formula $\sin$
+\end_inset
+
+,
+\begin_inset Formula $\lim$
+\end_inset
+
+,
+\emph on
+etc
+\emph default
+.
+ (you can also insert them in a formula by typing
+\series bold
+
+\backslash
+sin
+\series default
+ etc.).
+ Standard mathematical practice is that functions are printed upright to
+ avoid confusions, because
+\begin_inset Formula $sin$
+\end_inset
+
+ does normally mean
+\begin_inset Formula $s\cdot i\cdot n$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Using the function macros will also produce correct spacing around the function:
+
+\begin_inset Formula $a\sin x$
+\end_inset
+
+ is different from
+\begin_inset Formula $asinx$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+For some mathematical objects, like limits, the macro changes where subscripts
+ are placed, as described in section
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Operators-with-Limits"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Accents
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Accents
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In a formula you can insert accented characters in the same way as in text
+ mode.
+ This may depend on your keyboard, or the bindings file you use.
+ You can also use \SpecialChar LaTeX
+ commands, for example, to enter
+\begin_inset Formula $\hat{a}$
+\end_inset
+
+ even if your keyboard doesn't have the circumflex enabled.
+ Our example is entered by typing
+\series bold
+
+\backslash
+hat
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+a
+\series default
+ in a formula.
+ Table
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "tab:Accent-names-and"
+
+\end_inset
+
+ shows the equivalences between the accent names and the commands.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float table
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "tab:Accent-names-and"
+
+\end_inset
+
+Accent names and the corresponding commands.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="11" columns="3">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Name
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+E
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+xample
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+circumflex
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+hat
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+\begin_inset Formula $\hat{a}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+grave
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+grave
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+\begin_inset Formula $\grave{a}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+acute
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+acute
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+\begin_inset Formula $\acute{a}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+umlaut
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+ddot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+\begin_inset Formula $\ddot{a}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+tilde
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+tilde
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+\begin_inset Formula $\tilde{a}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+dot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+dot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+\begin_inset Formula $\dot{a}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+breve
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+breve
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+\begin_inset Formula $\breve{a}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+caron
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+check
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+\begin_inset Formula $\check{a}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+macron
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+bar
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+\begin_inset Formula $\bar{a}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+vector
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+vec
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+\begin_inset Formula $\vec{a}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You can choose one of the accents by selecting an item from the
+\family sans
+Frame
+\begin_inset space ~
+\end_inset
+
+decorations
+\family default
+ symbol set button
+\begin_inset Info
+type "icon"
+arg "math-insert \\hat"
+\end_inset
+
+ in the math panel; this will apply to any selection you have made within
+ a formula too.
+\end_layout
+
+\begin_layout Section
+Brackets and Delimiters
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Brackets
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Delimiters
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Brackets-and-Delimiters"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+There are several brackets available through \SpecialChar LyX
+.
+ For some purposes, using just the keys
+\family typewriter
+[]{}()|<>
+\family default
+ should suffice.
+ But if you want to surround a large structure, like a matrix or a fraction,
+ or if you have several layers of brackets, it is better to use the math
+ toolbar delimiter icon
+\begin_inset Info
+type "icon"
+arg "dialog-show mathdelimiter"
+\end_inset
+
+.
+ For example, if you construct the brackets around a matrix in this way:
+\begin_inset Formula
+\[
+\left[\begin{array}{cc}
+1 & 2\\
+3 & 4
+\end{array}\right]
+\]
+
+\end_inset
+
+it makes it easier to see the layers of parentheses.
+ Below, the expression on the left was entered using the delimiter icon
+
+\begin_inset Info
+type "icon"
+arg "dialog-show mathdelimiter"
+\end_inset
+
+ and the expression on the right was entered using the
+\family typewriter
+()
+\family default
+ keys.
+
+\begin_inset Formula
+\[
+\frac{1}{\left(1+\left(\frac{1}{1+\left(\frac{1}{1+x}\right)}\right)\right)}\qquad\qquad\frac{1}{(1+(\frac{1}{1+(\frac{1}{1+x})}))}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+If you use the delimiter icon, the parentheses, and other brackets from
+ that menu will automatically re-size to accommodate the size of what is
+ inside.
+\end_layout
+
+\begin_layout Standard
+To construct brackets click on the button for the bracket you want on the
+ left side and right side.
+ If you use the option
+\family sans
+Keep
+\begin_inset space ~
+\end_inset
+
+matched
+\family default
+, the selected bracket type will be used for the left and the right side.
+ The selection will be shown as \SpecialChar TeX
+ code.
+ If you want one side not to have a bracket, use
+\family sans
+(none)
+\family default
+.
+ It will appear in \SpecialChar LyX
+ with a dotted line, but nothing will be printed.
+\end_layout
+
+\begin_layout Standard
+If you want to place brackets around existing math structures, like a square
+ root, you can do so by first highlighting (selecting) the structure that
+ is to go inside the brackets.
+ Then choose the appropriate brackets for left and right and click on
+\family sans
+Insert
+\family default
+.
+ The most common bracket combinations (parentheses, square brackets, and
+ braces, on both sides) can be entered more quickly using keyboard shortcuts.
+ For example, to insert a pair of parentheses, select the structure and
+ enter
+\begin_inset Info
+type "shortcut"
+arg "math-delim ( )"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Arrays and Multi-line Equations
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Arrays
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Matrices
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Multi-line Equations
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Matrices are entered in \SpecialChar LyX
+ using the
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Panel
+\family default
+ matrix button
+\begin_inset Info
+type "icon"
+arg "dialog-show mathmatrix"
+\end_inset
+
+.
+ It will open a dialog for you to choose the number of rows/columns.
+ Here is an example:
+\begin_inset Formula
+\[
+\left(\begin{array}{ccc}
+1 & 2 & 3\\
+4 & 5 & 6\\
+7 & 8 & 9
+\end{array}\right)
+\]
+
+\end_inset
+
+The parentheses aren't automatic, but you can add them as described in section
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Brackets-and-Delimiters"
+
+\end_inset
+
+.
+ When you construct the matrix, you can decide whether the column entries
+ will be left-, right-, or center-justified.
+ This alignment is set in the box
+\family sans
+Horizontal
+\family default
+ with the letters
+\begin_inset Quotes eld
+\end_inset
+
+
+\family sans
+l
+\family default
+
+\begin_inset Quotes erd
+\end_inset
+
+,
+\begin_inset Quotes eld
+\end_inset
+
+
+\family sans
+r
+\family default
+
+\begin_inset Quotes erd
+\end_inset
+
+, and
+\begin_inset Quotes eld
+\end_inset
+
+
+\family sans
+c
+\family default
+
+\begin_inset Quotes erd
+\end_inset
+
+.
+ \SpecialChar LyX
+ proposes a
+\begin_inset Quotes eld
+\end_inset
+
+
+\family sans
+c
+\family default
+
+\begin_inset Quotes erd
+\end_inset
+
+ for every column as default.
+ For example, the sequence
+\begin_inset Quotes eld
+\end_inset
+
+
+\family sans
+lcr
+\family default
+
+\begin_inset Quotes erd
+\end_inset
+
+ means that the first column will be left-justified, the second will be
+ centered, and the third column will be right-justified, because each letter
+ corresponds to the relevant column.
+ The result will look like this:
+\begin_inset Formula
+\[
+\begin{array}{lcr}
+this & this\,column & this\,column\\
+column & has & has\,right\\
+has\,left\,alignment & center\,alignment & alignment
+\end{array}.
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You can add more rows to an existing matrix by entering
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+ while the cursor is in the matrix.
+ Adding or deleting columns can be done via the menu
+\family sans
+Edit\SpecialChar menuseparator
+Math
+\family default
+ or the math toolbar.
+\end_layout
+
+\begin_layout Standard
+There are other arrays used in formulas, such as distinctions of cases.
+ It can be created with the menu
+\family sans
+Insert\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Cases
+\begin_inset space ~
+\end_inset
+
+Environment
+\family default
+ or the command
+\series bold
+
+\backslash
+cases
+\series default
+.
+ Here is an example:
+\begin_inset Formula
+\[
+f(x)=\begin{cases}
+-1 & x<0\\
+0 & x=0\\
+1 & x>0
+\end{cases}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Multi-line formulas are created when you press
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+ within a formula.
+ In an empty formula you can see that three blue boxes appear, one for each
+ column.
+ When you press
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+ in a non-empty formula, the part before the relation sign (equal sign
+\begin_inset Quotes eld
+\end_inset
+
+=
+\begin_inset Quotes erd
+\end_inset
+
+ etc.) will be inserted automatically in the first column, the relation sign
+ is in the second column, and the rest in the third column.
+ A new row is created by every further entry of
+\begin_inset Info
+type "shortcut"
+arg "newline-insert newline"
+\end_inset
+
+.
+ Multi-line formulas are always displayed formulas.
+ Here is an example:
+\begin_inset Formula
+\begin{eqnarray}
+a^{2} & = & (b^{2}+c^{2})(b^{2}-c^{2})\nonumber \\
+a & = & \sqrt{b^{4}-c^{4}}\label{eq:asquared}
+\end{eqnarray}
+
+\end_inset
+
+Note that the middle column is designed for relation signs so structures
+ in this column will be printed in a smaller size:
+\begin_inset Formula
+\begin{eqnarray*}
+\frac{A}{B} & \frac{A}{B} & \frac{A}{B}
+\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The multi-line formula type described here is called
+\family typewriter
+\series medium
+eqnarray
+\family default
+\series default
+.
+ There are other multi-line types more suitable for certain situations,
+ for example if you want a better inter-line spacing than in formula
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:asquared"
+
+\end_inset
+
+.
+ The other types are described in section
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:AMS-Formula-Types"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Formula Numbering and Referencing
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Formula numbering
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Math ! Referencing formulas
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Formula-Numbering-and"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To number a formula, set the cursor in the formula and use the menu
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Number
+\begin_inset space ~
+\end_inset
+
+Whole
+\begin_inset space ~
+\end_inset
+
+Formula
+\family default
+ or the shortcut
+\begin_inset Info
+type "shortcut"
+arg "math-number-toggle"
+\end_inset
+
+.
+ The formula number appears in \SpecialChar LyX
+ within parentheses.
+ The number shown is temporary and may be different when the output is generated.
+ The placement and format of the formula number in the output depends on
+ the document class.
+ In this document the number is printed together with the chapter number,
+ separated by a dot:
+\begin_inset Formula
+\begin{equation}
+1+1=2
+\end{equation}
+
+\end_inset
+
+Using
+\begin_inset Info
+type "shortcut"
+arg "math-number-toggle"
+\end_inset
+
+ in a numbered formula will switch off the numbering.
+ You can only number displayed formulas.
+\end_layout
+
+\begin_layout Standard
+Multi-line formulas can be numbered line by line: Using the menu
+\family sans
+Edit\SpecialChar menuseparator
+Math\SpecialChar menuseparator
+Number
+\begin_inset space ~
+\end_inset
+
+This
+\begin_inset space ~
+\end_inset
+
+Line
+\family default
+ or the shortcut
+\begin_inset Info
+type "shortcut"
+arg "math-number-line-toggle"
+\end_inset
+
+ will only toggle the numbering of the line where the cursor is:
+\begin_inset Formula
+\begin{eqnarray}
+1 & = & 3-2\\
+2 & = & 4-2\nonumber \\
+4 & \leq & 7
+\end{eqnarray}
+
+\end_inset
+
+To number all lines use the shortcut
+\begin_inset Info
+type "shortcut"
+arg "math-number-toggle"
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Every displayed formula can be referenced by its number using a label.
+ A label is inserted with the menu
+\family sans
+Insert\SpecialChar menuseparator
+Label
+\family default
+ (toolbar button
+\begin_inset Info
+type "icon"
+arg "label-insert"
+\end_inset
+
+) when the cursor is in the formula.
+ This opens a dialog to enter the label.
+ It is recommended that you use the suggested
+\begin_inset Quotes eld
+\end_inset
+
+
+\family sans
+eq:
+\family default
+
+\begin_inset Quotes erd
+\end_inset
+
+ as the first part of the label, because this helps later to identify the
+ label type when you have many labels in your document.
+ We inserted in the following example the label
+\begin_inset Quotes eld
+\end_inset
+
+eq:tanhExp
+\begin_inset Quotes erd
+\end_inset
+
+ in the second line:
+\begin_inset Formula
+\begin{eqnarray}
+\tanh(x) & = & \frac{\sinh(x)}{\cosh(x)}\nonumber \\
+ & = & \frac{\mathrm{e}^{2x}-1}{\mathrm{e}^{2x}+1}\label{eq:tanhExp}
+\end{eqnarray}
+