نمایش مختصر رکورد

dc.contributor.authorKhosravi, M.en_US
dc.contributor.authorSheikhhosseini, A.en_US
dc.date.accessioned1399-07-08T21:11:14Zfa_IR
dc.date.accessioned2020-09-29T21:11:14Z
dc.date.available1399-07-08T21:11:14Zfa_IR
dc.date.available2020-09-29T21:11:14Z
dc.date.issued2015-09-01en_US
dc.date.issued1394-06-10fa_IR
dc.date.submitted2015-09-07en_US
dc.date.submitted1394-06-16fa_IR
dc.identifier.citationKhosravi, M., Sheikhhosseini, A.. (2015). Schur multiplier norm of product of matrices. Wavelet and Linear Algebra, 2(1), 49-54.en_US
dc.identifier.issn2383-1936
dc.identifier.issn2476-3926
dc.identifier.urihttp://wala.vru.ac.ir/article_14269.html
dc.identifier.urihttps://iranjournals.nlai.ir/handle/123456789/104863
dc.description.abstract<span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">For <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>A </em><span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">∈ <span style="font-family: MSBM10; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">M <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>n</em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">, the Schur multiplier of <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>A </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">is defined as <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>S </em><span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>A</em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">(<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>X</em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">) <span style="font-family: rtxr; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">= <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>A </em><span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">◦ <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>X </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">for all <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>X </em><span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">∈ <span style="font-family: MSBM10; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">M <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>n </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">and the spectral norm of <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>S </em><span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>A </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">can be state <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">as <span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">∥<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>S </em><span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>A</em><span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">∥ <span style="font-family: rtxr; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">= <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">sup<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>X</em><span style="font-family: txsyc; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">,<span style="font-family: NimbusRomNo9L-Regu; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">0 <span style="font-family: txsy; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">∥<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>A </em><span style="font-family: txsy; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">∥<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>X </em><span style="font-family: txsy; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">◦<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>X </em><span style="font-family: txsy; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">∥ ∥<span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">. The other norm on <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>S </em><span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>A </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">can be defined <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">as <span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">∥<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>S </em><span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>A</em><span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">∥<span style="font-family: rtxmi; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">ω <span style="font-family: rtxr; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">= <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">sup<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>X</em><span style="font-family: txsyc; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">,<span style="font-family: NimbusRomNo9L-Regu; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">0 <span style="font-family: rtxmi; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">ω<span style="font-family: NimbusRomNo9L-Regu; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">(<span style="font-family: rtxmi; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">ω <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>S</em><span style="font-family: NimbusRomNo9L-Regu; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">( <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 5pt; color: #000000; font-style: normal; font-variant: normal;"><em>A</em><span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>X </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">(<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>X </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">) )) <span style="font-family: rtxr; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">= <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">sup<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>X</em><span style="font-family: txsyc; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">,<span style="font-family: NimbusRomNo9L-Regu; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">0 <span style="font-family: rtxmi; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">ωω <span style="font-family: NimbusRomNo9L-Regu; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">(<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>A </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">(<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>X </em><span style="font-family: txsy; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">◦<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>X </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">) )<span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">, where <span style="font-family: rtxmi; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">ω<span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">(<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>A</em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">) stands <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">for the numerical radius of <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>A</em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">. In this paper, we focus on the <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">relation between the norm of Schur multiplier of product of matrices and the product of norm of those matrices. This relation is <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">proved for Schur product and geometric product and some applications are given. Also we show that there is no such relation <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">for operator product of matrices. Furthermore, for positive definite matrices <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>A </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">and <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>B </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">with <span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">∥<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>S </em><span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>A</em><span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">∥<span style="font-family: rtxmi; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">ω <span style="font-family: MSAM10; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">⩽ <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">1 and <span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">∥<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>S </em><span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>B</em><span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">∥<span style="font-family: rtxmi; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">ω <span style="font-family: MSAM10; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">⩽ <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">1, we show <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">that <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>A</em><span style="font-family: rtxmi; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">♯<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>B </em><span style="font-family: rtxr; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">= <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>n</em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">(<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>I </em><span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">− <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>Z</em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">)<span style="font-family: NimbusRomNo9L-Regu; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">1<span style="font-family: rtxmi; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">/<span style="font-family: NimbusRomNo9L-Regu; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">2<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>C</em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">(<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>I </em><span style="font-family: rtxr; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">+ <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>Z</em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">)<span style="font-family: NimbusRomNo9L-Regu; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">1<span style="font-family: rtxmi; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">/<span style="font-family: NimbusRomNo9L-Regu; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">2<span style="font-family: rtxmi; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">, <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">for some contraction <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>C </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">and <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">Hermitian contraction <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>Z</em><span style="font-family: rtxmi; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>en_US
dc.format.extent1431
dc.format.mimetypeapplication/pdf
dc.languageEnglish
dc.language.isoen_US
dc.publisherVali-e-Asr university of Rafsanjanen_US
dc.relation.ispartofWavelet and Linear Algebraen_US
dc.relation.ispartofموجک و جبر خطیfa_IR
dc.subjectSchur multiplieren_US
dc.subjectSchur producten_US
dc.subjectGeometric producten_US
dc.subjectPositive semidefinite matrixen_US
dc.subjectNumerical radiusen_US
dc.titleSchur multiplier norm of product of matricesen_US
dc.typeTexten_US
dc.typeResearch Paperen_US
dc.contributor.departmentShahid Bahonar university of Kermanen_US
dc.contributor.departmentShahid Bahonar university of Kermanen_US
dc.citation.volume2
dc.citation.issue1
dc.citation.spage49
dc.citation.epage54


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