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Core and core-EP inverses of tensors

Abstract

Specific definitions of the core and core-EP inverses of complex tensors are introduced. Some characterizations, representations and properties of the core and core-EP inverses are investigated. The results are verified using specific algebraic approach, based on proposed definitions and previously verified properties. The approach used here is new even in the matrix case.

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Acknowledgements

Ratikanta Behera acknowledges the support provided by Science and Engineering Research Board (SERB), Department of Science and Technology, India, under the Grant No. EEQ/2017/000747.

Predrag Stanimirović gratefully acknowledges support from the Ministry of Education, Science and Technological Development, Republic of Serbia, Grant No. 174013.

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Correspondence to Predrag S. Stanimirović.

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Communicated by Jinyun Yuan.

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Sahoo, J.K., Behera, R., Stanimirović, P.S. et al. Core and core-EP inverses of tensors. Comp. Appl. Math. 39, 9 (2020). https://doi.org/10.1007/s40314-019-0983-5

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  • DOI: https://doi.org/10.1007/s40314-019-0983-5

Keywords

  • Generalized inverse
  • Core-EP inverse
  • Core inverse
  • Tensor
  • Einstein product

Mathematics Subject Classification

  • 15A69
  • 15A09