| Sumario: | This paper de nes for the rst time strong linearizations of arbitrary rational ma- trices, studies in depth properties and characterizations of such linear matrix pencils, and develops in nitely many examples of strong linearizations that can be explicitly and easily constructed from a minimal state-space realization of the strictly proper part of the considered rational matrix and the coe cients of the polynomial part. As a consequence, the results in this paper establish a rigorous foundation for the numerical computation of the complete structure of zeros and poles, both nite and at in nity, of any rational matrix by applying any well-known backward stable algorithm for generalized eigenvalue problems to any of the strong linearizations constructed in this work.
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