目的深入刻画线性空间C^(n)与M_(n)中常见的重要的范数的对偶范数。方法利用对偶范数定义及范数的特性,通过Holder不等式、对偶原理、排序不等式、奇异值的Weyl不等式及Neumann不等式进行研究。结果给出C^(n)上l_(p)-范数与k-范数及M_(n...目的深入刻画线性空间C^(n)与M_(n)中常见的重要的范数的对偶范数。方法利用对偶范数定义及范数的特性,通过Holder不等式、对偶原理、排序不等式、奇异值的Weyl不等式及Neumann不等式进行研究。结果给出C^(n)上l_(p)-范数与k-范数及M_(n)上Schatten p-范数和Ky Fan k-范数的表示,并给出M_(n)上算子范数的特性。结论完善了线性空间C^(n)与M_(n)中对偶范数的性质,为利用范数解决数值计算问题奠定了理论基础。展开更多
In this paper, the unitarily invariant norm \\.\\ on C-mxn is used. We first discuss the problem under what case, a rectangular matrix A has minimum condition number K(A) = \\A\\ \\A(+)\\, where A(+) designates the Mo...In this paper, the unitarily invariant norm \\.\\ on C-mxn is used. We first discuss the problem under what case, a rectangular matrix A has minimum condition number K(A) = \\A\\ \\A(+)\\, where A(+) designates the Moore-Penrose inverse of A; and under what condition, a square matrix A has minimum condition number for its eigenproblem? Then we consider the second problem, i.e., optimum of K(A) = \\A\\ \\A(-1)\\(2) in error estimation.展开更多
We consider maps on positive definite cones of von Neumann algebras preserving unitarily invariant norms of the spectral geometric means. The main results concern Jordan *-isomorphisms between <em>C</em>*-...We consider maps on positive definite cones of von Neumann algebras preserving unitarily invariant norms of the spectral geometric means. The main results concern Jordan *-isomorphisms between <em>C</em>*-algebras, and show that they are characterized by the preservation of unitarily invariant norms of those operations.展开更多
The optimal preconditioner and the superoptimal preconditioner were proposed in 1988 and 1992 respectively. They have been studied widely since then. Recently, Chen and Jin [6] extend the superoptimal preconditioner t...The optimal preconditioner and the superoptimal preconditioner were proposed in 1988 and 1992 respectively. They have been studied widely since then. Recently, Chen and Jin [6] extend the superoptimal preconditioner to a more general case by using the Moore-Penrose inverse. In this paper, we further study some useful properties of the optimal and the generalized superoptimal preconditioners. Several existing results are extended and new properties are developed.展开更多
基金Supported by the Fund for Fostering Talents in Kunming University of Science and Technology(KKZ3202007048)the National Natural Science Foundation of China(11801240)。
文摘目的深入刻画线性空间C^(n)与M_(n)中常见的重要的范数的对偶范数。方法利用对偶范数定义及范数的特性,通过Holder不等式、对偶原理、排序不等式、奇异值的Weyl不等式及Neumann不等式进行研究。结果给出C^(n)上l_(p)-范数与k-范数及M_(n)上Schatten p-范数和Ky Fan k-范数的表示,并给出M_(n)上算子范数的特性。结论完善了线性空间C^(n)与M_(n)中对偶范数的性质,为利用范数解决数值计算问题奠定了理论基础。
文摘In this paper, the unitarily invariant norm \\.\\ on C-mxn is used. We first discuss the problem under what case, a rectangular matrix A has minimum condition number K(A) = \\A\\ \\A(+)\\, where A(+) designates the Moore-Penrose inverse of A; and under what condition, a square matrix A has minimum condition number for its eigenproblem? Then we consider the second problem, i.e., optimum of K(A) = \\A\\ \\A(-1)\\(2) in error estimation.
文摘We consider maps on positive definite cones of von Neumann algebras preserving unitarily invariant norms of the spectral geometric means. The main results concern Jordan *-isomorphisms between <em>C</em>*-algebras, and show that they are characterized by the preservation of unitarily invariant norms of those operations.
基金supported by the research grant UL020/08-Y2/MAT/ JXQ01/FST from University of Macao
文摘The optimal preconditioner and the superoptimal preconditioner were proposed in 1988 and 1992 respectively. They have been studied widely since then. Recently, Chen and Jin [6] extend the superoptimal preconditioner to a more general case by using the Moore-Penrose inverse. In this paper, we further study some useful properties of the optimal and the generalized superoptimal preconditioners. Several existing results are extended and new properties are developed.
基金supported by the National Natural Science Foundation of China(11571220)the Natural Scientific Research Project of Fuyang Normal University(2016FSKJ20)
