- #1

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consider two following partitioned matrices:

[tex]\begin{array}{l}

{M_1} = \left[ {\begin{array}{*{20}{c}}

{ - \frac{1}{2}{X_1}} & {{X_2}} \\

{{X_3}} & { - \frac{1}{2}{X_4}} \\

\end{array}} \right] \\

{M_2} = \left[ {\begin{array}{*{20}{c}}

{\begin{array}{*{20}{c}}

{{X_1}} & { - I} \\

I & 0 \\

\end{array}} & {\begin{array}{*{20}{c}}

0 & 0 \\

0 & 0 \\

\end{array}} \\

{\begin{array}{*{20}{c}}

0 & 0 \\

0 & 0 \\

\end{array}} & {\begin{array}{*{20}{c}}

{{X_4}} & { - I} \\

I & 0 \\

\end{array}} \\

\end{array}} \right] \\

\end{array}[/tex]

I want to show that spectral radius (maximum absolute value of eigenvalues) of M1 and M2 are equal, but I don't know how!!!!!!!!!

this is general form of my problem the real one is somewhat easier (or maybe more complex)!!!