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July 11th, 2010, 10:42 PM   #1
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Roots of a system of equations

Hi everyone,

I'm an electrical engineering student. during performing my thesis, on computational methods in electromagnetics, I encounter following problem.

suppose following equation (roots of a second order equation):

z = ( 2*G-F +/- sqrt(F^2-8*F*G) ) / (2*F+2*G)

where F is symmetric and positive semi-definite and G is symmetric and positive definite. we also know that (F^2-8*F*G) > 0.

how it can be proofed that abs(z)<1 ?

If it can be proofed it's a great help to me.

thanks a lot,
ali987 is offline  
 
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