Resonance frequency of a matrix system

PlpPlp

Hi all,

I have a 2d system of the form:

dm1/dt + A11 m1 + A12 m2 = 0
dm2/dt + A21 m2 + A22 m2 = 0

I saw that the resonance frequency of such a system is defined as:

fr = 1/(2*pi) [ (A11 + A22)/2 + sqrt( ((A11-A22)/2)^2 + A12*A21 )

if I'm not mistaking - I can't even remember where I saw that formula.

Could someone confirm that it's the exact formula and/or explain why this holds and how this was obtained and/or how does this extend to the 3d case?

Thanks a lot!