[翻譯]Arthur Cayley，矩陣理論紀要(A Memoir on the Theory of Matrices)，part: 2

The notion of such a matrix arises naturally from an abbreviated notation for a set of linear equations, viz. the equations
$$\begin{eqnarray*} X &=& ax+by+cz,\\ Y &=& a'x+b'y+c'z\\ Z &=& a''x+b''y+c''z \end{eqnarray*}$$
may be more simply represented by
$$\left[ \begin{array}{c} X \\ Y \\ Z \end{array} \right] = \left[ \begin{array}{ccc} a & b & c \\ a' & b' & c' \\ a'' & b'' & c'' \end{array} \right] \left[ \begin{array}{c} x \\ y \\ z \end{array} \right]$$
and the consideration of such a system of equations leads to most of the fundamental notions in the theory of matrices.

矩陣的概念係由簡記一組線性方程式自然派生而出，所謂線性方程式，例如
$$\begin{eqnarray*} X &=& ax+by+cz,\\ Y &=& a'x+b'y+c'z\\ Z &=& a''x+b''y+c''z \end{eqnarray*}$$

可簡記為

$$\left[ \begin{array}{c} X \\ Y \\ Z \end{array} \right] = \left[ \begin{array}{ccc} a & b & c \\ a' & b' & c' \\ a'' & b'' & c'' \end{array} \right] \left[ \begin{array}{c} x \\ y \\ z \end{array} \right]$$

而關於線性方程組的研究，引領出矩陣理論中最基本的幾個概念。