grandes-ecoles 2017 Q6

grandes-ecoles · France · x-ens-maths__pc Matrices Eigenvalue and Characteristic Polynomial Analysis
Determine the spectral radius of the following matrices $$\left( \begin{array} { l l } 0 & 0 \\ 0 & 1 \end{array} \right) , \quad \left( \begin{array} { l l } 0 & 0 \\ 1 & 0 \end{array} \right) , \quad \left( \begin{array} { l l } 1 & 0 \\ 0 & 0 \end{array} \right) , \quad \left( \begin{array} { c c } 0 & - 1 \\ 2 & 0 \end{array} \right) , \quad \left( \begin{array} { l l } 3 & 2 \\ 1 & 2 \end{array} \right)$$
Determine the spectral radius of the following matrices
$$\left( \begin{array} { l l } 
0 & 0 \\
0 & 1
\end{array} \right) , \quad \left( \begin{array} { l l } 
0 & 0 \\
1 & 0
\end{array} \right) , \quad \left( \begin{array} { l l } 
1 & 0 \\
0 & 0
\end{array} \right) , \quad \left( \begin{array} { c c } 
0 & - 1 \\
2 & 0
\end{array} \right) , \quad \left( \begin{array} { l l } 
3 & 2 \\
1 & 2
\end{array} \right)$$