Trace and determinant preserving maps of matrices

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• 作者：Huajun Huang^a ; ^{huanghu@auburn.edu" class="auth_mail" title="E-mail the corresponding author} ; Chih-Neng Liu^b ; ^{cnliu@mail.nsysu.edu.tw" class="auth_mail" title="E-mail the corresponding author} ; Patrí ; cia Szokol^c ; ^d ; ^{matszp@uni-miskolc.hu" class="auth_mail" title="E-mail the corresponding author} ; ^{szokolp@science.unideb.hu" class="auth_mail" title="E-mail the corresponding author} ; Ming-Cheng Tsai^e ; ^{mctsai2@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Jun Zhang^f ; ^{zhjun@mail.ccnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A15 ; 47B49 ; 15A04
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 October 2016
• 年：2016
• 卷：507
• 期：Complete
• 页码：373-388
• 全文大小：372 K

文摘

We show that if a map ϕ on the set of positive definite matrices satisfies then ϕ   is of the form class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302403&_mathId=si2.gif&_user=111111111&_pii=S0024379516302403&_rdoc=1&_issn=00243795&md5=f64accf5a230b237bed81a00c0c3b70f" title="Click to view the MathML source">ϕ(A)=M^⁎AMclass="mathContainer hidden">class="mathCode">$\varphi (A)=M^{⁎}AM$ or class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302403&_mathId=si24.gif&_user=111111111&_pii=S0024379516302403&_rdoc=1&_issn=00243795&md5=1333dab2b0ec564ee7e0feba4c640a98" title="Click to view the MathML source">ϕ(A)=M^⁎A^tMclass="mathContainer hidden">class="mathCode">$\varphi (A)=M^{⁎}{A}^{t}M$ for some invertible matrix M   with class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302403&_mathId=si158.gif&_user=111111111&_pii=S0024379516302403&_rdoc=1&_issn=00243795&md5=71149d4f10bbad555d7da644bca9e943" title="Click to view the MathML source">det⁡(M^⁎M)=1class="mathContainer hidden">class="mathCode">$\det (M^{⁎}M)=1$. We also characterize the map class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302403&_mathId=si5.gif&_user=111111111&_pii=S0024379516302403&_rdoc=1&_issn=00243795&md5=8538e2357e694faa882abc949be46387" title="Click to view the MathML source">ϕ:S→Sclass="mathContainer hidden">class="mathCode">$\varphi :\mathcal{S}\to \mathcal{S}$ preserving the similar trace equality or the determinant equality

in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302403&_mathId=si7.gif&_user=111111111&_pii=S0024379516302403&_rdoc=1&_issn=00243795&md5=bc9c9ccfeee18592478b3d847a13dc9c" title="Click to view the MathML source">Sclass="mathContainer hidden">class="mathCode">$\mathcal{S}$, where class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302403&_mathId=si7.gif&_user=111111111&_pii=S0024379516302403&_rdoc=1&_issn=00243795&md5=bc9c9ccfeee18592478b3d847a13dc9c" title="Click to view the MathML source">Sclass="mathContainer hidden">class="mathCode">$\mathcal{S}$ denotes the set of complex matrices, symmetric matrices, or upper triangular matrices, respectively.