Frontiers of Mathematics in China >
lk,s-Singular values and spectral radius of partially symmetric rectangular tensors
Received date: 02 Mar 2015
Accepted date: 05 Jun 2015
Published date: 17 May 2016
Copyright
The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. In this paper, we first study properties of lk,s-singular values of real rectangular tensors. Then, a necessary and sufficient condition for the positive definiteness of partially symmetric rectangular tensors is given. Furthermore, we show that the weak Perron-Frobenius theorem for nonnegative partially symmetric rectangular tensor keeps valid under some new conditions and we prove a maximum property for the largest lk,s-singular values of nonnegative partially symmetric rectangular tensor. Finally, we prove that the largest lk,ssingular value of nonnegative weakly irreducible partially symmetric rectangular tensor is still geometrically simple.
Hongmei YAO , Bingsong LONG , Changjiang BU , Jiang ZHOU . lk,s-Singular values and spectral radius of partially symmetric rectangular tensors[J]. Frontiers of Mathematics in China, 2016 , 11(3) : 605 -622 . DOI: 10.1007/s11464-015-0494-7
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