[翻譯]Arthur Cayley，矩陣理論紀要(A Memoir on the Theory of Matrices)，part: 3

It will be seen that matrices (attending only to those of the same order) comport themselves as single quantities; they may be added, multiplied or compounded together, &c.: the law of the addition of matrices is precisely similar to that for the addition of ordinary algebraical quantities; as regards their multiplication (or composition), there is the peculiarity that matrices are not in general convertible; it is nevertheless possible to form the powers (positive or negative, integral of fractional) of a matrix, and thence to arrive at the notion of a rational and integral function, or generally of any algebraical function, of a matrix.

我們可將矩陣與矩陣視作一般的量(quantity)來計算(限於同尺寸之矩陣)；矩陣與矩陣彼此可相加、相乘，或是複合(compound，同時進行加法與乘法)等等: 矩陣的加法與我們平素所考慮的代數量的加法雷同；而矩陣的乘法(或是所謂的「合成(composition)」)，必須注意到一個特異點是，一般說來，矩陣必非總是可逆的。不過我們仍然可以考慮矩陣的冪(正數或負數、整數或分數)，順藤摸瓜就引入了以矩陣為變量的有理函數或是整函數，甚或任意代數函數。