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118 results on '"Huang, Shaowu"'

1. Majorization in some symplectic weak supermajorizations

Author

Huang, Shaowu and Mishra, Hemant K.

Subjects
Mathematics - Functional Analysis, Mathematical Physics, Mathematics - Symplectic Geometry, Mathematics - Spectral Theory, Quantum Physics, 15B48, 15A18
Abstract

Symplectic eigenvalues are known to satisfy analogs of several classic eigenvalue inequalities. Of these is a set of weak supermajorization relations concerning symplectic eigenvalues that are weaker analogs of some majorization relations corresponding to eigenvalues. The aim of this letter is to establish necessary and sufficient conditions for the saturation of the symplectic weak supermajorization relations by majorization., Comment: 8 pages, The old version had some typos that are corrected in the new version. The typos were in Eq.(1.14) and Eq.(1.23). Also, proof of Corollary 1.5 is added in the new version. Accepted in Linear Algebra and its Applications. June 2024

Published
2024
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2. Inequalities on generalized matrix functions

Author

Huang, Shaowu, Li, Chi-Kwong, Poon, Yiu-Tung, and Wang, Qing-Wen

Subjects
Mathematics - Functional Analysis, 15A15, 15A45, 15A63, 15B57
Abstract

We prove inequalities on non-integer powers of products of generalized matrices functions on the sum of positive semi-definite matrices. For example, for any real number $r \in \{1\} \cup [2, \infty)$, positive semi-definite matrices $A_i,\ B_i,\ C_i\in M_{n_i}$, $i=1,2$, and generalized matrix functions $d_\chi, d_\xi$ such as the determinant and permanent, etc., we have \begin{eqnarray*}&&\left(d_\chi(A_1+B_1+C_1)d_\xi(A_2+B_2+C_2)\right)^r \\ &&\hskip 1in + \left(d_\chi(A_1)d_\xi(A_2)\right)^r + \left(d_\chi(B_1)d_\xi(B_2)\right)^r + \left(d_\chi(C_1)d_\xi(C_2)\right)^r \\ & \ge &\left(d_\chi(A_1+B_1 )d_\xi(A_2+B_2 )\right)^r + \left(d_\chi(A_1+ C_1)d_\xi(A_2+ C_2)\right)^r + \left(d_\chi( B_1+C_1)d_\xi( B_2+C_2)\right)^r\,.\end{eqnarray*} A general scheme is introduced to prove more general inequalities involving $m$ positive semi-definite matrices for $m \ge 3$ that extend the results of other authors., Comment: 15 pages

Published
2016

3. Another proof of a result on the doubly superstochastic matrices.

Author

Huang, Shaowu

Subjects
*MATRICES (Mathematics), *EIGENVALUES, *MATHEMATICS
Abstract

We establish a trace inequality of symplectic matrices via a more general trace minimization theorem. As a consequence, we derive another proof of a result in [R. Bhatia, T. Jain, On symplectic eigenvalues of positive-definite matrices, J. Math. Phys., 56 (2015),112201.]. [ABSTRACT FROM AUTHOR]

Published
2024
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6. Extensions of pseudo-Perron-Frobenius splitting related to generalized inverse AT,S(2)

Author

Huang Shaowu, Wang Qing-Wen, Wu Shuxia, and Yu Yaoming

Subjects
proper splitting, perron-frobenius splitting, outer-perron-frobenius splitting, generalized inverse, cones of matrices, 15a09, 15b48, Mathematics, QA1-939
Abstract

We in this paper define the outer-Perron-Frobenius splitting, which is an extension of the pseudo- Perron-Frobenius splitting defined in [A.N. Sushama, K. Premakumari, K.C. Sivakumar, Extensions of Perron-Frobenius splittings and relationships with nonnegative Moore-Penrose inverse, Linear and Multilinear Algebra 63 (2015) 1-11]. We present some criteria for the convergence of the outer-Perron-Frobenius splitting. The findings of this paper generalize some known results in the literatures.

Published
2018
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11. A new version of Schur–Horn type theorem.

Author

Huang, Shaowu

Subjects
*LINEAR algebra, *EIGENVALUES
Abstract

In this paper, we establish a new version of a Schur–Horn type theorem. Meanwhile, we provide a new proof of a recent result in [Bhatia R, Jain T. A Schur-Horn theorem for symplectic eigenvalues. Linear Algebra Appl. 2020;599:133–139]. [ABSTRACT FROM AUTHOR]

Published
2023
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14. A Quick Screening of High Yield Strength Points in Single-Phase Co-Cr-Fe-Ni-Mo High Entropy Alloy System Based on Electronegativity, Thermodynamic Calculations and Machine Learning

Author

Song, Zijing, primary, Fang, Wei, additional, Yan, Jiaohui, additional, Chang, Ruobin, additional, Huang, Shaowu, additional, Shi, Yating, additional, Zheng, Tianyuan, additional, Yu, Haoyang, additional, Bai, Xi, additional, Liu, Baoxi, additional, and Yin, Fuxing, additional

Published
2020
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41. Equivalence on some Rotfel’d type theorems.

Author

Huang, Shaowu, Wang, Qing-Wen, and Zhang, Yang

Subjects
*MATHEMATICAL equivalence, *MATHEMATICS theorems, *CONCAVE functions, *MATHEMATICAL proofs, *FIELD extensions (Mathematics)
Abstract

In this paper, we prove that some recent Rotfel’d theorem extensions are equivalent. [ABSTRACT FROM AUTHOR]

Published
2018
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42. Proper Splitting for the Generalized Inverse ${A}_{T,S}^{(2)}$ and Its Application on Banach Spaces

Author

Liu, Xiaoji and Huang, Shaowu

Abstract

A possible type of the operator splitting is studied. Using this operator splitting, we introduce some properties and representations of generalized inverses as well as iterative method for computing various solutions of the restricted linear operator system $Ax=b, x\in T$ , where $A\in {\scr L}(\textbf{X},\textbf{Y})$ and T is an arbitrary but fixed subspace of X.

Published
2012

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