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- W4287979441 abstract "A complete theory of the relationship between the minimal bases and indices of rational matrices and those of their strong linearizations is presented. Such theory is based on establishing first the relationships between the minimal bases and indices of rational matrices and those of their polynomial system matrices under the classical minimality condition and certain additional conditions of properness. This is related to pioneer results obtained by Verghese, Van Dooren and Kailath in 1979-80, which were the first proving results of this type under different nonequivalent conditions. It is shown that the definitions of linearizations and strong linearizations do not guarantee any relationship between the minimal bases and indices of the linearizations and the rational matrices in general. In contrast, simple relationships are obtained for the family of strong block minimal bases linearizations, which can be used to compute minimal bases and indices of any rational matrix, including rectangular ones, via algorithms for pencils. These results extend the corresponding ones for other families of linearizations available in recent literature for square rational matrices." @default.
- W4287979441 created "2022-07-26" @default.
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- W4287979441 date "2019-12-27" @default.
- W4287979441 modified "2023-09-23" @default.
- W4287979441 title "On minimal bases and indices of rational matrices and their linearizations" @default.
- W4287979441 doi "https://doi.org/10.48550/arxiv.1912.12293" @default.
- W4287979441 hasPublicationYear "2019" @default.
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