On two classes of matrices with positive diagonal solutions to the Lyapunov equation

Abstract We characterize real indecomposable quasi-Jacobi matrices of class D , i.e., those which satisfy the Lyapunov equation PA + A′P = −Q with P diagonal and both P and Q positive definite. The subclass D 2 (of class D ) when also Q is diagonal is also characterized in the case of general indecomposable real matrices.

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