# Math Help - Eigenvalues of a matrix involved in a linear matrix equality

1. ## Eigenvalues of a matrix involved in a linear matrix equality

We know that:

with , e : matrixes $\in\Re^{nxn}$; : generic eigenvalue of A;

To be proved:

with : positive scalar;

Writing with ,

we can prove , because .

How to link eigenvalues of A to $\overline{Q}$?

2. How about taking the "known" result (for matrices satisfying $A^{\textsc t}P + PA = -Q$ ), and applying it with $A+cI$ in place of $A$?

3. You are right, good suggestion!