In this paper,we study real symmetric Toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric Toeplitz matrices. Also, complex Toeplitz ...In this paper,we study real symmetric Toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric Toeplitz matrices. Also, complex Toeplitz matrices, especially the corresponding matrices of lower order, are discussed.展开更多
Let Q be the quaternion division algebra over real field F, Denote by Hn（Q） the set of all n x n hermitian matrices over Q. We characterize the additive maps from Hn（Q） into Hm（Q） that preserve rank-1 matrices w...Let Q be the quaternion division algebra over real field F, Denote by Hn（Q） the set of all n x n hermitian matrices over Q. We characterize the additive maps from Hn（Q） into Hm（Q） that preserve rank-1 matrices when the rank of the image of In is equal to n. Let QR be the quaternion division algebra over the field of real number R. The additive maps from Hn （QR） into Hm （QR） that preserve rank-1 matrices are also given.展开更多
To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There a...To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different approaches to find such metric operators. We compare the different approaches of calculating positive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations. Exceptional points and spontaneous symmetry breaking are also discussed in these models.展开更多
文摘In this paper,we study real symmetric Toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric Toeplitz matrices. Also, complex Toeplitz matrices, especially the corresponding matrices of lower order, are discussed.
文摘Let Q be the quaternion division algebra over real field F, Denote by Hn（Q） the set of all n x n hermitian matrices over Q. We characterize the additive maps from Hn（Q） into Hm（Q） that preserve rank-1 matrices when the rank of the image of In is equal to n. Let QR be the quaternion division algebra over the field of real number R. The additive maps from Hn （QR） into Hm （QR） that preserve rank-1 matrices are also given.
文摘To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different approaches to find such metric operators. We compare the different approaches of calculating positive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations. Exceptional points and spontaneous symmetry breaking are also discussed in these models.
