Combined matrices of sign regular matrices

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• 作者：Rafael Bru^a ; ^{rbru@mat.upv.es" class="auth_mail" title="E-mail the corresponding author} ; Maria T. Gassó ; ^a ; ^{mgasso@mat.upv.es" class="auth_mail" title="E-mail the corresponding author} ; Isabel Gimé ; nez^a ; ^{igimenez@mat.upv.es" class="auth_mail" title="E-mail the corresponding author} ; Má ; ximo Santana^b ; ^{msantana22@uasd.edu.do" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A48 ; 15A57
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 June 2016
• 年：2016
• 卷：498
• 期：Complete
• 页码：88-98
• 全文大小：308 K

文摘

The combined matrix of a nonsingular matrix A   is the Hadamard (entry wise) product class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379514008003&_mathId=si1.gif&_user=111111111&_pii=S0024379514008003&_rdoc=1&_issn=00243795&md5=5e66bc0f0ea2f4e59e91ca7197b23350" title="Click to view the MathML source">C(A)=A∘(A⁻¹)^Tclass="mathContainer hidden">class="mathCode">$C(A)=A\circ {(A^{-1})}^T$. Since each row and column sum of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379514008003&_mathId=si2.gif&_user=111111111&_pii=S0024379514008003&_rdoc=1&_issn=00243795&md5=c2c5804794c8cc1ccacb9aceaee5afbe" title="Click to view the MathML source">C(A)class="mathContainer hidden">class="mathCode">$C(A)$ is equal to one, the combined matrix is doubly stochastic when it is nonnegative. In this work, we study the nonnegativity of the combined matrix of sign regular matrices, based upon their signature. In particular, a few coordinates of the signature ε of A   play a crucial role in determining whether or not class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379514008003&_mathId=si2.gif&_user=111111111&_pii=S0024379514008003&_rdoc=1&_issn=00243795&md5=c2c5804794c8cc1ccacb9aceaee5afbe" title="Click to view the MathML source">C(A)class="mathContainer hidden">class="mathCode">$C(A)$ is nonnegative.