Extremal values of the trace norm over oriented trees

详细信息    查看全文

• 作者：N. Agudelo^a ; ^{nagudel83@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; J.A. de la Peñ ; a^b ; ^{jap@cimat.mx" class="auth_mail" title="E-mail the corresponding author} ; J. Rada^a ; ^{pablo.rada@udea.edu.co" class="auth_mail" title="E-mail the corresponding author}
• 关键词：05C50
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 September 2016
• 年：2016
• 卷：505
• 期：Complete
• 页码：261-268
• 全文大小：290 K

文摘

The trace norm of the digraph D   is defined as class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516301525&_mathId=si1.gif&_user=111111111&_pii=S0024379516301525&_rdoc=1&_issn=00243795&md5=0992e8c20e6ae11de6ed856ea0440c6a">class="imgLazyJSB inlineImage" height="35" width="106" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0024379516301525-si1.gif">class="mathContainer hidden">class="mathCode">$\mathcal{N}\left(D\right)=\sum _{i=1}^n{\sigma }_i$, where class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516301525&_mathId=si2.gif&_user=111111111&_pii=S0024379516301525&_rdoc=1&_issn=00243795&md5=2e922844319182f746c7648b6429240c" title="Click to view the MathML source">σ₁≥σ₂≥⋯≥σ_n≥0class="mathContainer hidden">class="mathCode">${\sigma }_1\ge {\sigma }_2\ge \cdots \ge {\sigma }_n\ge 0$ are the singular values of the adjacency matrix A of D  , i.e. the square roots of the eigenvalues of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516301525&_mathId=si3.gif&_user=111111111&_pii=S0024379516301525&_rdoc=1&_issn=00243795&md5=7e491f2dc8f31c22fb521cbdff1be93b" title="Click to view the MathML source">AA^⊤class="mathContainer hidden">class="mathCode">$A{A}^{\top }$. We find the extremal values of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516301525&_mathId=si14.gif&_user=111111111&_pii=S0024379516301525&_rdoc=1&_issn=00243795&md5=570acf07d121022de55161dfde57f4e8" title="Click to view the MathML source">Nclass="mathContainer hidden">class="mathCode">$\mathcal{N}$ over the set of oriented trees and over the set of oriented paths.