Eigenvalues of a special complex matrix


1.09.2009

Hello,

I have the following problem:

Let F be a full square real matrix, and D be a diagonal real matrix.
Then we construct a complex matrix
C = F + z*D
where z is a complex parameter.
I need to determine eigenvalues of C. Are there any theorems
that can be applied to find out whether the eigenvalues
may have any special properties?
For example, can one say anything general about the dependence of the eigenvalues on z,
and on the location of the eigenvalues
relative to z, in the complex plane?

Please point me to any potentially helpful literature.

Leslaw
.

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