We shall give natural generalized solutions of Hadamard and tensor products equations for matrices by the concept of the Tikhonov regularization combined with the theory of reproducing kernels.
A short description of structural and virtual Kirichenko tensors that form a complete system of first-order differential-geometrical invariants of an arbitrary almost Hermitian structure is given.A characterization of...A short description of structural and virtual Kirichenko tensors that form a complete system of first-order differential-geometrical invariants of an arbitrary almost Hermitian structure is given.A characterization of nearly-Khlerian structures in terms of Kirichenko tensors is also given.展开更多
The Hermitian tensor is an extension of Hermitian matrices and plays an important role in quantum information research.It is known that every symmetric tensor has a symmetric CP-decomposition.However,symmetric Hermiti...The Hermitian tensor is an extension of Hermitian matrices and plays an important role in quantum information research.It is known that every symmetric tensor has a symmetric CP-decomposition.However,symmetric Hermitian tensor is not the case.In this paper,we obtain a necessary and sufficient condition for symmetric Hermitian decomposability of symmetric Hermitian tensors.When a symmetric Hermitian decomposable tensor space is regarded as a linear space over the real number field,we also obtain its dimension formula and basis.Moreover,if the tensor is symmetric Hermitian decomposable,then the symmetric Hermitian decomposition can be obtained by using the symmetric Hermitian basis.In the application of quantum information,the symmetric Hermitian decomposability condition can be used to determine the symmetry separability of symmetric quantum mixed states.展开更多
文摘We shall give natural generalized solutions of Hadamard and tensor products equations for matrices by the concept of the Tikhonov regularization combined with the theory of reproducing kernels.
文摘A short description of structural and virtual Kirichenko tensors that form a complete system of first-order differential-geometrical invariants of an arbitrary almost Hermitian structure is given.A characterization of nearly-Khlerian structures in terms of Kirichenko tensors is also given.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11871472).
文摘The Hermitian tensor is an extension of Hermitian matrices and plays an important role in quantum information research.It is known that every symmetric tensor has a symmetric CP-decomposition.However,symmetric Hermitian tensor is not the case.In this paper,we obtain a necessary and sufficient condition for symmetric Hermitian decomposability of symmetric Hermitian tensors.When a symmetric Hermitian decomposable tensor space is regarded as a linear space over the real number field,we also obtain its dimension formula and basis.Moreover,if the tensor is symmetric Hermitian decomposable,then the symmetric Hermitian decomposition can be obtained by using the symmetric Hermitian basis.In the application of quantum information,the symmetric Hermitian decomposability condition can be used to determine the symmetry separability of symmetric quantum mixed states.
