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Properties of Some Classes of Structured Tensors

  • Yisheng SongEmail author
  • Liqun Qi
Article

Abstract

In this paper, we extend some classes of structured matrices to higher-order tensors. We discuss their relationships with positive semi-definite tensors and some other structured tensors. We show that every principal sub-tensor of such a structured tensor is still a structured tensor in the same class, with a lower dimension. The potential links of such structured tensors with optimization, nonlinear equations, nonlinear complementarity problems, variational inequalities and the non-negative tensor theory are also discussed.

Keywords

P tensor \(\hbox {P}_0\) tensor B tensor \(\hbox {B}_0\) tensor Principal sub-tensor Eigenvalues 

Mathematics Subject Classification (2010)

47H15 47H12 34B10 47A52 47J10 47H09 15A48 47H07 

Notes

Acknowledgments

The authors would like to thank the anonymous referees for their valuable suggestions which helped us to improve this manuscript.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceHenan Normal UniversityXinxiangPeople’s Republic of China
  2. 2.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityHung Hom, KowloonHong Kong

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