## Math Notation Help

<$$ Keyword(s): less than< #### less than or equal$$x\le~y$or x\leq~y$$gives $x\le~y$  Keyword(s): <= ### M #### math spaces List of predefined spaces:  Math Spaces Command Example Result \, (smallest predefined) $$a\,ba\,b$$ \: (second smallest predefined) $$a\:ba\:b$$ \; (third smallest predefined) $$a\;ba\;b\/ (avoiding ligatures)V\/A instead of$$VAV\/A$instead of$VA$$\quad (space of current character set size)$$a\quad~ba\quad~b$$\qquad (double space of current character set size)$$a\qquad~ba\qquad~b\_ (where _ is blank!)a\ b$(whereas $$a\bis not a valid filter expression since the blank space is missing; it is recommended to use the tilde ~ instead of the simple whitespace)a\ b\hspace{n} ,where n positive integer (= n Pixels)a~\hspace{30}~b$$$a~\hspace{15}~b$a~\hspace{2}~b$$$a~\hspace{1}~ba~\hspace{30}~b$$a~\hspace{15}~b$$a~\hspace{2}~b$$a~\hspace{1}~b\unitlength{m}\hspace{n}, changes the default unit length (m=1px) to be applieda~\hspace{2}~b\unitlength{10}~\hspace{2}~c(second space is 10x2=20px) $a~\hspace{2}~b\unitlength{10}~\hspace{2}~c$ Note: Simple blank spaces and tildes (~) are ignored by the TeX filter and don't produce any space. You must use one of the defined math spaces to get a visible (extra) space.  Keyword(s): spaces in formulas, predefined spaces #### mathematics expression • A valid expression inside the 's is rendered as mathematics in an inserted gif image. • Ex.:$$x=y^2creates x=y^2$$ Keyword(s): mathematics expression #### matrix • An (m,n)-matrix is considered as an array of m*n elements, where the elements of a column are separated by "&" and the rows by "\\". • Syntax for an (m,n)-matrix: \begin{array}{colformat}a11&...&a1n\\a21&...&a2n\\... \\am1&...&amn \end{array} where colformat defines the format of each of the n columns: l for left, r for right and c for center (hence {ccccc} defines for a (m,5)-matrix in which all columns are centered) • Ex.:$$\left(\begin{array}{lcr}a_{\tiny1}+d & a_{\tiny2}+d & a_{\tiny3}+d \\ b_{\tiny1}& b_{\tiny2}& b_{\tiny3} \\ c_{\tiny1} & c_{\tiny2} & c_{\tiny3} \end{array}\right)gives \left(\begin{array}{lcr}a_{\tiny1}+d & a_{\tiny2}+d & a_{\tiny3}+d \\ b_{\tiny1}& b_{\tiny2}& b_{\tiny3} \\ c_{\tiny1} & c_{\tiny2} & c_{\tiny3} \end{array}\right)$\$

Note in the example above that "lcr" has the effect that column 1 is left aligned, column 2 centered and colums 3 right aligned.

 Keyword(s): matrix, array

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