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Operations research, linear programming, control theory, systems theory, optimal control, game theory

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Prove that absolute value of eigenvalue is smaller than 1 [closed]

I want to prove that the absolute value of the eigenvalues of a matrix A are smaller than 1 for $$A=\left(\begin{array}{cc} 0 & -H_{11}^{-1} H_{12} \\ -H_{22}^{-1} H_{21} & 0 \end{array}\right)$$ I kn …