Determinants of Harmonic Matrices
J. S. MacNerney · Proceedings of the American Mathematical Society · 1956
This paper is concerned with extensions of a theorem by H. S. Wall (Theorem 3 of [3]) : if M is a 2 X2 harmonic matrix and F corresponds to M then det M= 1 only in case Fn= -F22.As in [3] let Hn denote the class of «X« harmonic matrices and $>" the class of nXn matrices F of complex-valued functions from the real numbers, continuous and of bounded variation on every interval, such that F(0) =0.In [3] Wall has shown that the Stieltjes integral equation,(1) Mis, t) = 2 + f dF(u)-M(u, I), defines a one-to-one correspondence M~F between H" and <£".In studying this correspondence in a more abstract setting, the present author [l] has obtained the continuous product (or "product integral") representation,(2) Mis, t) = JJ' [l + &} when M~F.