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Mathematicians in many disciplines like to construct rectangular arrays
of formulas that have been arranged in rows and columns; such an array
is called a {\it matrix}. Plain \TeX\ provides control sequences that
make most common types of matrices easy to print.
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You can print simple matrices to indicate their product:
$$\left(\matrix{a&amp;b&amp;c\cr
                  d&amp;e&amp;f\cr}\right) \left(\matrix{u&amp;x\cr
                                                 v&amp;y\cr
                                                 w&amp;z\cr}\right).$$
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More complex matrices are just as easy to print:
$$A=\left(\matrix{x-\lambda&amp;1&amp;0\cr
                   0&amp;x-\lambda&amp;1\cr
                   0&amp;0&amp;x-\lambda\cr}\right).$$
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Even genertic patterned matrices that use ellipses to indicate rows or columns
are simple to set up and print:
$$A=\pmatrix{a_{11}&amp;a_{12}&amp;\ldots&amp;a_{1n}\cr
             a_{21}&amp;a_{22}&amp;\ldots&amp;a_{2n}\cr
             \dots&amp;\vdots&amp;\ddots&amp;\vdots\cr
             a_{m1}&amp;a_{m2}&amp;\ldots&amp;a_{mn}\cr}.$$
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Determinants are constructed in much the same way with the same ease:
$$\det\left|\,\matrix{
               c_0&amp;c_1\hfill&amp;c_2\hfill&amp;\ldots&amp;c_n\hfill\cr
               c_1&amp;c_2\hfill&amp;c_3\hfill&amp;\ldots&amp;c_{n+1}\hfill\cr
               c_2&amp;c_3\hfill&amp;c_4\hfill&amp;\ldots&amp;c_{n+2}\hfill\cr
               \,\vdots\hfill&amp;\,\vdots\hfill&amp;\,\vdots\hfill&amp;&amp;\,\vdots\hfill\cr
               c_n&amp;c_{n+1}\hfill&amp;c_{n+2}\hfill&amp;\ldots&amp;c_{2n}\hfill\cr}\right|&gt;
0.$$
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