The authors supply an explicit procedure to construct reciprocal matrices realizing any desired orders for the right Perron vector and the entrywise inverse left Perron vector, with a concrete size-4 example that settles an open existence question.
Csat´ o,Right-left asymmetry of the eigenvector method: A simulation study, European Journal of Operational Research 313 (2024), 708-717
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Existence of reciprocal matrices with specified orders for the right and inverse left Perron eigenvectors
The authors supply an explicit procedure to construct reciprocal matrices realizing any desired orders for the right Perron vector and the entrywise inverse left Perron vector, with a concrete size-4 example that settles an open existence question.