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Factor and term ranks for matrix union over semirings

Abstract

We consider the arithmetic properties of the factor-rank and term-rank functions for matrices over semirings. In particular, we investigate the sets of matrices that satisfy the extremes of inequalities for these rank functions of matrix union. The classification of the linear transformations that keep these sets invariant is obtained.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 175–197, 2003.

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Pshenitsyna, O.A. Factor and term ranks for matrix union over semirings. J Math Sci 135, 3384–3399 (2006). https://doi.org/10.1007/s10958-006-0168-9

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Keywords

  • Linear Transformation
  • Rank Function
  • Matrix Union
  • Arithmetic Property
  • Term Rank