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VIII .4. M ATHEMATICS MISCELLANY

Here \dotsc stands for dots to be used with commas, \dotsb for dots with binary operations (or relations) and \dotsm for multiplication dots. There is also a \dotsi for dots with integrals as in Z A 1 Z A 2 · · · Z A n f

VIII . 4 . 3 . Delimiters How do we produce something like

a h g h b f g f c !

a h g h b f g f c

Since

= 0 , the matrix

is not invertible.

Here the ‘small’ in-text matrices are produced by the environment smallmatrix . This environment does not provide the enclosing delimiters ( ) or — — which we must supply as in $ \left|\begin{smallmatrix}

a & h & g\\ h & b & f\\ g & f & c \end{smallmatrix}\right|

=0 $, the matrix $ \left(\begin{smallmatrix}

a & h & g\\ h & b & f\\ g & f & c \end{smallmatrix}\right)

$ is not invertible.

Why the \left|...\right| and \left{...\right ? These commands \left and \right enlarge the delimiter following them to the size of the enclosed material. To see their ef- fect, try typesetting the above example without these commands. The list of symbols at the end of the chapter gives a list of delimiters that are available off the shelf. One interesting point about the \left and \right pair is that, though every \left should be matched to a \right , the delimiters to which they apply need not match. In par- ticular we can produce a single large delimiter produced by \left or \right by matching it with a matching command followed by a period. For example,

u x = v y u y = − v x )

Cauchy-Riemann Equations

is produced by