Sample of the day ---Operator names

Sample of the day ---Operator names

[David Arnold]

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\AmSTeX\ makes it easy to define new operator names.

\define\tr{\operatorname{Tr}}

The sum of the elements on the main diagonal is called the {\it
trace} of the matrix; i.e., if
$$
A=\pmatrix
a_{11} & a_{12} & \dots & a_{1n}\\
a_{21} & a_{22} & \dots & a_{2n}\\
\vdots & \vdots & \ddots & \vdots\\
a_{n1} & a_{n2} & \dots & a_{nn}
\endpmatrix,
$$
then
$$
\tr(A)=a_{11}+a_{22}+\cdots+a_{nn}.
$$

You can also declare operator names for use with limits.

\define\res{\operatornamewithlimits{Res}}

$$
\res_{x=0}\frac{f(x)}{x}
$$

If $\res_{x=0} f(x)/x$, \dots
\bye

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