Elementary Matrix Algebra
K. Holden, A. W. Pearson · 1992
A matrix is a rectangular array of elements in rows and columns. Examples of matrices are ( 1 0 0 1 )( a b c c c b 2a 2c b )( x 11 x 12 x 13 x 21 x 22 x 23 ) ]] <![CDATA[$$left( {\begin{array}{*{20}{c}} 1&0 \\ 0&1 \end{array}} \right)\left( {\begin{array}{*{20}{c}} a&b&c \\ c&c&b \\ {2a}{2c}&b \end{array}} \right)\left( {\begin{array}{*{20}{c}} {{x_{11}}}{{x_{12}}}{{x_{13}}} \\ {}{}{} \\ {{x_{21}}}{{x_{22}}}{{x_{23}}} \end{array}} \right)$$ which are rectangular arrays with 2 rows and 2 columns, 3 rows and 3 columns and 2 rows and 3 columns respectively. The order of a matrix is the number of rows and the number of columns, so that in the above examples the orders are (2 × 2) or (2 by 2), (3 × 3), and (2 × 3) respectively. The elements, which may be numbers or constants or variables, are enclosed between square brackets to signify that they must be considered as a whole and not individually. In contrast to the determinants of Chapter 1, a matrix does not have a single numerical value.