On Some Properties of the Max Algebra System Over Tensors

Authors

  • Ali Reza Shojaeifard Department of Mathematics and Statistics, Faculty of Basic Sciences, Imam Hossein Comprehensive University, Tehran, Iran.
  • Hamid Reza Afshin Department of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Islamic Republic of Iran.
Abstract:

Recently we generalized the max algebra system to the class of nonnegative  tensors. In this paper we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverse of tensors is characterized. Also we generalize the direct product of matrices to the direct product of tensors (of the same order, but may be different dimensions) and investigate its properties relevant to the spectral theory.

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Journal title

volume 12  issue 1

pages  1- 14

publication date 2018-11-01

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