Journal
LINEAR & MULTILINEAR ALGEBRA
Volume 64, Issue 4, Pages 686-698Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/03081087.2015.1083933
Keywords
tensor; Moore-Penrose inverse; multilinear system
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Funding
- National Natural Science Foundation of China [11371109, 11271084]
- Natural Science Foundation of Heilongjiang Province [QC2014C001]
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In this paper, we define the Moore-Penrose inverse of tensors with the Einstein product, and the explicit formulas of the Moore-Penrose inverse of some block tensors are obtained. The general solutions of some multilinear systems are given and we also give the minimum-norm least-square solution of some multilinear systems using the Moore-Penrose inverse of tensors.
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