
Evaluation of a complex matrix by noninteger power indices
Posted:
Sep 28, 2013 6:34 AM


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 Sparameters for Nport 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?
Cheers, Julian
PS Anyone know of a forum where they provide mathematical notation?

