JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (4): 39-45.doi: 10.6040/j.issn.1671-9352.0.2020.422

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Structure of semilinear spaces based on semi-tensor addition

LI Xiao-chao   

  1. School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, Henan, China
  • Published:2021-04-13

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Abstract: Semi-tensor addition of matrices is a generalization of the usual matrix addition. Based on the semi-tensor addition of matrices, the matrix semilinear spaces on nonnegative real number semiring are obtained. The dimension, basis and direct sum of the matrix semilinear spaces are researched, and a necessary and sufficient condition for the sum of two subspaces to be a direct sum is given.

Key words: semi-tensor addition, semilinear space, dimension, direct sum

CLC Number: 

  • O153
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