Evaluation of the square root of a complex matrix

I'll take on the easy, last question. Perhaps upload a pdf of the equation(s) to DropBox and provide a secure link, e.g.,

That lets you use the full power of LaTeX to compose it, notes and all. Or, for a quick'n'dirty equation, EqualX uses LaTeX math mode commands and you can \mbox{} a short note if required.

and maybe...

or...

Looks like it requires "recursive" approaches... i.e. guessing solutions ;-) ...Jim Thompson

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Have a look at:

Bell Systems Technical Journal, (1941), Rice, S.O.,v.20,p.131-178. for a matrix solution of transmission lines.

I wrote a paper in 1950 on an extension to n-wire lines, in which the square root of a complex matrix was involved. In this case the root is unique, but in general it may not be.

--
Virg Wall

I think the only book I have that goes into matrix square roots is Dan Simon's book on Kalman filtering.

You might ask on sci.electronics.design or comp.dsp -- this isn't a basic question!!

Note that this is a USENET newsgroup, and is therefor text-only. Usually if there's a lot of math being flung around people will use LaTeX format, or pseudo-LaTeX. You can generally make yourself understood.

--
Tim Wescott 
Control system and signal processing consulting 
www.wescottdesign.com

If you just want to numerically evaluate a result, you may simply use octave (or Matlab)

octave:1> sqrt([1 j;2 j]) ans =

1.00000 + 0.00000i 0.70711 + 0.70711i 1.41421 + 0.00000i 0.70711 + 0.70711i

If you want to derive the whole expression, I would investigate the meaning of the parameters instead of relying on pure algebra. For instance, the relation between Z and S parameters given in the wikipedia

Z=sqrt(z)*(1+S)(1-S)^(-1)*sqrt(z)

is just the vectorial generalization of the scalar equation

Z=Z0*(1+ro)/(1-ro)

I know that this is not the equation you are looking for, but the idea may be a starting point.

Pere

Thank you, gentlemen one and all, for your kind and helpful responses. I am evaluating your advice, as time permits, and hope to upload a pdf file of the excerpt from Abrie, 2009, sec 1.5 to Dropbox soon.

Kind regards,

Julian Grodzicky