University of MaraghehSahand Communications in Mathematical Analysis2322-580712120181101On Some Properties of the Max Algebra System Over Tensors1143002310.22130/scma.2018.30023ENAli Reza ShojaeifardDepartment of Mathematics and Statistics, Faculty of Basic Sciences, Imam Hossein Comprehensive University, Tehran, Iran.Hamid Reza AfshinDepartment of Mathematics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Islamic Republic of Iran.Journal Article20170406Recently 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.http://scma.maragheh.ac.ir/article_30023_8488dc3d5ca759a228ad5df74c6ba29b.pdf