Summary: How do I evaluate the square root of a complex matrix?
I am studying from Pieter LD Abrie's "Design of RF and Microwave Amplifiers and Oscillators", 2ed, Artech House, 2009.
In the first chapter he presents derivations of S-parameters for N-port networks (sec. 1.5), he states an expression on page 13, (sqrt(2))^(-1)*[Z_0 + Z_0*]^(1/2), where the matrix of impedances is Z_0 = [R_0i + jX_0i], and Z_0* is the complex conjugate matrix of Z_0; j=sqrt(-1); R_0i is the ith resistance of port i and X_0i is the ith reactance of port i.
I'm trying to derive this expression, but all the texts on Linear Algebra that I have in my personal library only deal with positive integer powers of real matrices. (I have in my arsenal "Elementary Linear Algebra: Applications Version", H.Anton & C.Rorres, 6ed, Wiley: "Schaum's Outline of Linear Algebra; "Mathematical Methods for Physics and Engineering", 2ed, K.F.Riley, M.P.Hobson & S.J.Bence, Cambridge UP).
What topics and texts do I need to study to be able to evaluate the square root of a complex matrix?
PS Anyone know of a forum where they provide mathematical notation?