Publication: A matrix Euclidean algorithm induced by state space realization
A matrix Euclidean algorithm induced by state space realization
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Allen, B., & Rosenthal, J. (1999). A matrix Euclidean algorithm induced by state space realization. Linear Algebra and Its Applications, 288(1–3), 105–121. https://doi.org/10.1016/S0024-3795(98)10186-6
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An efficient algorithm is developed for determining the greatest common left divisor (GCLD) of two polynomial matrices. Knowing this divisor allows for several immediate applications. In coding theory, a noncatastrophic convolutional encoder can be derived from an arbitrary one. In systems theory, irreducible matrix fraction descriptions of transfer function matrices can be found. In linear algebra, the greatest common divisor can be seen as a basis for a free module generated by the columns of the matrices. The approach taken is base
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- Rosenthal, J
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Allen, B., & Rosenthal, J. (1999). A matrix Euclidean algorithm induced by state space realization. Linear Algebra and Its Applications, 288(1–3), 105–121. https://doi.org/10.1016/S0024-3795(98)10186-6
