Hi everyone,(adsbygoogle = window.adsbygoogle || []).push({});

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)!!!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Help me on finding spectral radius!

**Physics Forums | Science Articles, Homework Help, Discussion**