HELP:Physical meaning MoM matrix eigenvalues

physical meaning of eigenvalue

Hi all,
I'm analyzing FSS structure.
The MoM analysis is based on Electric Field Integral Equation (EFIE) and leads to the formulation of a homogeneous matrix problem (Z*I=0).
The solution of this problem is performed by an iterative procedure:
for a given value of the propagation phase constant beta,
the frequency range is scanned to find the frequencies where the field equation has a non trivial solution.
The search of these frequency is based on the detection of the determinant zero crossing.

In the slow region(no radiation), the Z (anti-hermitian) eigenvalues are pure imaginary.
In the fast region(radiation), the Z (general complex) eigenvalues are complex.
While frequency's increasing eigenvalues are decreasing (so they couldn't be propagation constants-like).

What is the physical meaning of Z eigenvalues?

Thanks in advance!

Regards.

physical meaning of matrix

kalo said:

Hi all,

In the slow region(no radiation), the Z (anti-hermitian) eigenvalues are pure imaginary.
In the fast region(radiation), the Z (general complex) eigenvalues are complex.
While frequency's increasing eigenvalues are decreasing (so they couldn't be propagation constants-like).

Click to expand...

what is the reason for these statements? is it true for all eigenvalues for the nxn matrix?

physical meaning of eigenvalues

MoM uses rooftop basis functions.
The matrix elements are definited so that Z matrix is anti-hermitian (in the slow region).
So, nxn anti-hermitian matrix has got n pure imaginary eigenvalues.

matrix physical meaning

can you point me to a reference where the above statement is made/proved?

I have some idea on the rooftop basis, I only know that the matrix is symmetric (complex). I don't know how you can give physical meaning to all of the n eigenvalues.