﻿ 域上矩阵保乘积的诱导映射

# 域上矩阵保乘积的诱导映射Induced Maps Preserving Multiplicative Matrices over Fields

Abstract: Let F be a field, S
n(F) be the set of all n*n matrices over F. If a map f:Sn(F)→Sn(F) is defined by ∫:B=(bij)|→(fij(bij))
where {fij|i≤j∈{1,2,...,n}} is the set of functions on F, then f is called a map induced by {fij} on Sn(F). If A,B∈Sn(F) implies f(AB)=f(A)f(B), then f is called preserving multiplicative matrices. In this paper, we characterize induced maps preserving multiplicative matrices over fields.

[1] Li, C.K., Plevnik, L. and Semrl, P. (2012) Preservers of Matrix Pairs with a Fixed Inner Product Value. Operators and Matrices, 6, 433-464.

[2] Cao, C.G., Ge, Y.L. and Yao, H.M. (2013) Maps Preserving Classical Adjoint of Products of Two Matrices. Linear and Multilinear Algebra, 61, 1593-1604.
http://dx.doi.org/10.1080/03081087.2012.753592

[3] Huang, L.P. (2006) Geometry of Matrices over Ring. Science Press.

[4] You, H. and Wang, Z.Y. (2007) k-Potence Preserving Maps without the Linearty and Surjectivity Assumptions. Linear Algebra and Its Applications, 426, 238-254.
http://dx.doi.org/10.1016/j.laa.2007.04.024

[5] Chooi, W.L. and Ng, W.S. (2010) On Classical Ad-joint-Commuting Mappings between Matrix Algebras. Linear Algebra and Its Applications, 432, 2589-2599.
http://dx.doi.org/10.1016/j.laa.2009.12.001

[6] Liu, S.W. and Zhang, G.D. (2006) Maps Preserving Rank $1$ Matrices over Fields. Journal of Natural Science of Heilongjiang University, 23, 138-140.

[7] Yang, L., Ben, X.Z., Zhang, M. and Cao, C.G. (2014) Induced Maps on Matrices over Fields. Abstract and Applied Analysis, 2014, Article ID: 596796.

Top