In this paper,we study some inclusion sets of US-eigenvalues and U-eigenvalues based on quantum information.We give three inclusion sets theorems of US-eigenvalues and two inclusion sets theorems of U-eigenvalues.And ...In this paper,we study some inclusion sets of US-eigenvalues and U-eigenvalues based on quantum information.We give three inclusion sets theorems of US-eigenvalues and two inclusion sets theorems of U-eigenvalues.And we obtain the relationships among these inclusion sets.Some numerical examples are shown to illustrate the conclusions.展开更多
In this paper, we introduce the complex completely positive tensor, which has a symmetric complex decomposition with all real and imaginary parts of the decomposition vectors being non-negative. Some properties of the...In this paper, we introduce the complex completely positive tensor, which has a symmetric complex decomposition with all real and imaginary parts of the decomposition vectors being non-negative. Some properties of the complex completely positive tensor are given. A semidefinite algorithm is also proposed for checking whether a complex tensor is complex completely positive or not. If a tensor is not complex completely positive, a certificate for it can be obtained;if it is complex completely positive, a complex completely positive decomposition can be obtained.展开更多
In this paper,we introduce the almost unitarily decomposable conjugate partial-symmetric tensors,which are different from the commonly studied orthogonally decomposable tensors by involving the conjugate terms in the ...In this paper,we introduce the almost unitarily decomposable conjugate partial-symmetric tensors,which are different from the commonly studied orthogonally decomposable tensors by involving the conjugate terms in the decomposition and the perturbation term.We not only show that successive rank-one approximation algorithm exactly recovers the unitary decomposition of the unitarily decomposable conjugate partial-symmetric tensors.The perturbation analysis of successive rank-one approximation algorithm for almost unitarily decomposable conjugate partial-symmetric tensors is also provided to demonstrate the robustness of the algorithm.展开更多
基金supported in part by the National Natural Science Foundation of China(No.12071097)the Joint Guidance Natural Science Foundation of Heilongjiang Province of China(No.LH2021A004)the Basic Scientific Research Foundation of National Defense(No.JCKYS2021604SSJS002)
文摘In this paper,we study some inclusion sets of US-eigenvalues and U-eigenvalues based on quantum information.We give three inclusion sets theorems of US-eigenvalues and two inclusion sets theorems of U-eigenvalues.And we obtain the relationships among these inclusion sets.Some numerical examples are shown to illustrate the conclusions.
基金National Natural Science Foundation of China (Grant No. 11701356)supported by National Natural Science Foundation of China (Grant No. 11571234)+2 种基金supported by National Natural Science Foundation of China (Grant No. 11571220)National Postdoctoral Program for Innovative Talents (Grant No. BX201600097)China Postdoctoral Science Foundation (Grant No. 2016M601562)。
文摘In this paper, we introduce the complex completely positive tensor, which has a symmetric complex decomposition with all real and imaginary parts of the decomposition vectors being non-negative. Some properties of the complex completely positive tensor are given. A semidefinite algorithm is also proposed for checking whether a complex tensor is complex completely positive or not. If a tensor is not complex completely positive, a certificate for it can be obtained;if it is complex completely positive, a complex completely positive decomposition can be obtained.
基金This work was partially supported by the National Natural Science Foundation of China(No.11571234).
文摘In this paper,we introduce the almost unitarily decomposable conjugate partial-symmetric tensors,which are different from the commonly studied orthogonally decomposable tensors by involving the conjugate terms in the decomposition and the perturbation term.We not only show that successive rank-one approximation algorithm exactly recovers the unitary decomposition of the unitarily decomposable conjugate partial-symmetric tensors.The perturbation analysis of successive rank-one approximation algorithm for almost unitarily decomposable conjugate partial-symmetric tensors is also provided to demonstrate the robustness of the algorithm.
