On matrices whose coefficients are functions of a single variable
J. H. M. Wedderburn · Transactions of the American Mathematical Society · 1915
1. The methods usually* employed in reducing to its normal form a matrix whose coefficients are polynomials in a variable X are of such a nature that it is not at all obvious how they can be extended when polynomials are replaced by analytic functions.t The object of this note is to show that the main theorems on elementary factors are not restricted to matric polynomials but apply without appreciable modification to analytic matric functions. As vectors are employed freely in the sequel, a short explanation of the notation used is necessary. A vector, x = (t1, 62, * * *, in) is an ordered set of n coefficients: two vectors are equal if, and only if, their corresponding coefficients are equal. The sum of two vectors, x = n t2, * , n) and y = (, 772, *, n) is defined as