scholarly journals Linear preservers on matrices

1987 ◽  
Vol 93 ◽  
pp. 67-80 ◽  
Author(s):  
Gin-Hor Chan ◽  
Ming-Huat Lim ◽  
Kok-Keong Tan
Keyword(s):  
Linear Preservers

scholarly journals Linear preservers on triangular matrices

1998 ◽  
Vol 269 (1-3) ◽  
pp. 241-255 ◽  
Author(s):  
W.L. Chooi ◽  
M.H. Lim
Keyword(s):  
Triangular Matrices ◽  
Linear Preservers

scholarly journals Linear preservers of minimal rank

2000 ◽  
Vol 310 (1-3) ◽  
pp. 73-82 ◽  
Author(s):  
Leiba Rodman ◽  
Peter Šemrl
Keyword(s):  
Minimal Rank ◽  
Linear Preservers

scholarly journals Linear maps preserving rank 2 on the space of alternate matrices and their applications

2004 ◽  
Vol 2004 (63) ◽  
pp. 3409-3417 ◽  
Author(s):  
Chongguang Cao ◽  
Xiaomin Tang
Keyword(s):  
Linear Space ◽  
Linear Preservers ◽  
Linear Maps ◽  
Rank 2

Denote by𝒦n(F)the linear space of alln×nalternate matrices over a fieldF. We first characterize all linear bijective maps on𝒦n(F)(n≥4)preserving rank 2 whenFis any field, and thereby the characterization of all linear bijective maps on𝒦n(F)preserving the max-rank is done whenFis any field except for{0,1}. Furthermore, the linear preservers of the determinant (resp., adjoint) on𝒦n(F)are also characterized by reducing them to the linear preservers of the max-rank whennis even andFis any field except for{0,1}. This paper can be viewed as a supplement version of several related results.

scholarly journals Linear preservers and quantum information science

2013 ◽  
Vol 61 (10) ◽  
pp. 1377-1390 ◽  
Author(s):  
Ajda Fošner ◽  
Zejun Huang ◽  
Chi-Kwong Li ◽  
Nung-Sing Sze
Keyword(s):  
Quantum Information ◽  
Information Science ◽  
Quantum Information Science ◽  
Linear Preservers

scholarly journals Linear preservers of row-dense matrices

2016 ◽  
Vol 66 (3) ◽  
pp. 847-858 ◽  
Author(s):  
Sara M. Motlaghian ◽  
Ali Armandnejad ◽  
Frank J. Hall
Keyword(s):  
Linear Preservers ◽  
Dense Matrices

Linear preservers of Hadamard majorization

2016 ◽  
Vol 31 ◽  
pp. 593-609 ◽  
Author(s):  
Sara Motlaghian ◽  
Ali Armandnejad ◽  
Frank Hall
Keyword(s):  
Stochastic Matrix ◽  
Doubly Stochastic Matrix ◽  
Graph Theoretic ◽  
Doubly Stochastic ◽  
Linear Preservers ◽  
Linear Maps ◽  
Term Rank

Let $\textbf{M}_{n }$ be the set of all $n \times n $ realmatrices. A matrix $D=[d_{ij}]\in\textbf{M}_{n } $ with nonnegative entries is called doubly stochastic if $\sum_{k=1}^{n} d_{ik}=\sum_{k=1}^{n} d_{kj}=1$ for all $1\leq i,j\leq n$. For $ X,Y \in \textbf{M}_{n}$ we say that $X$ is Hadamard-majorized by $Y$, denoted by $ X\prec_{H} Y$, if there exists an $n \times n$ doubly stochastic matrix $D$ such that $X=D\circ Y$.In this paper, some properties of$\prec_{H}$ on $\textbf{M}_{n}$ are first obtained, and then the (strong) linear preservers of$\prec_{H}$ on $\textbf{M}_{n }$ are characterized. For $n\geq3$, it is shown that the strong linear preservers of Hadamard majorization on $\textbf{M}_{n}$ are precisely the invertible linear maps on $\textbf{M}_{n}$ which preserve the set of matrices of term rank 1.An interesting graph theoretic connection to the linear preservers of Hadamard majorization is exhibited. A number of examples are also provided in the paper.

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