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Matrix pencil equivalents of general polynomial matrix. (English) Zbl 0683.93015
O. H. Bosgra and A. J. J. van der Weiden [ibid. 33, 393-411 (1981; Zbl 0464.93021)] have given a procedure whereby a general polynomial system matrix may be reduced to an equivalent generalized state-space form. The sense in which this is equivalent to the original system matrix is that the reduced system exhibits identical system properties both at finite and infinite frequencies.
In the present work, a version of this algorithm appropriate to the matrix theory case will be presented, and it will be seen that this permits the reduction of a general polynomial matrix to a similarly equivalent matrix pencil form (i.e. one which exhibits identical finite and infinite zero struture). A description of this equivalence in a matrix transformational sense will also be given and in this respect it will be seen that the recently introduced transformation of full equivalence [the first and third author and P. Fretwell, ibid. 47, No.1, 53-64 (1988; Zbl 0661.93016)] plays an essential role.
Although essentially algebraic, the results of this paper further indicate the relevance of full equivalence to the systems theory context.

MSC:
93B17 Transformations
65F30 Other matrix algorithms (MSC2010)
15A22 Matrix pencils
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