| dc.contributor.author | Khalooei, F. | en_US |
| dc.date.accessioned | 1399-07-08T21:11:13Z | fa_IR |
| dc.date.accessioned | 2020-09-29T21:11:13Z | |
| dc.date.available | 1399-07-08T21:11:13Z | fa_IR |
| dc.date.available | 2020-09-29T21:11:13Z | |
| dc.date.issued | 2014-08-01 | en_US |
| dc.date.issued | 1393-05-10 | fa_IR |
| dc.date.submitted | 2014-07-01 | en_US |
| dc.date.submitted | 1393-04-10 | fa_IR |
| dc.identifier.citation | Khalooei, F.. (2014). Linear preservers of two-sided matrix majorization. Wavelet and Linear Algebra, 1(1), 43-50. | en_US |
| dc.identifier.issn | 2383-1936 | |
| dc.identifier.issn | 2476-3926 | |
| dc.identifier.uri | http://wala.vru.ac.ir/article_6350.html | |
| dc.identifier.uri | https://iranjournals.nlai.ir/handle/123456789/104856 | |
| dc.description.abstract | <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">For vectors <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>X</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>Y </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;">R<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;">, it is said that <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;">is left matrix majorized <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">by <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>Y </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">if for some row stochastic matrix <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>R</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: 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>RY</em><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;">The relation <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: rtxmi; font-size: 7pt; 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>Y</em><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;">is defined as follows: <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: rtxmi; font-size: 7pt; 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>Y </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">if and only if <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;">is left <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">matrix majorized by <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>Y </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>Y </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">is left matrix majorized by <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>X</em><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;">A <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">linear operator <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>T </em><span style="font-family: NimbusRomNo9L-Regu; 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;">R<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>p </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;">R<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;">is said to be a linear preserver of <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">a given relation <span style="font-family: txsy; 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;">if <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: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>Y </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">on <span style="font-family: MSBM10; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">R<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>p </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">implies that <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>T X </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>TY </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">on <span style="font-family: MSBM10; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">R<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 linear preservers of <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;">` <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">from <span style="font-family: MSBM10; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">R<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>p </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">to <span style="font-family: MSBM10; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">R<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;">are characterized <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">before. In this parer we characterize the linear preservers of <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;">` <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">from <span style="font-family: MSBM10; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">R<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>p </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">to <span style="font-family: MSBM10; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">R<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>n</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>p </em><span style="font-family: txsy; 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;">3<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;">In fact we show that the linear preservers <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">of <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;">` <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">from <span style="font-family: MSBM10; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">R<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>p </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">to <span style="font-family: MSBM10; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">R<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;">are the same as the linear preservers of <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;">` <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">from <span style="font-family: MSBM10; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">R<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>p </em><span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">to <span style="font-family: MSBM10; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">R<span style="font-family: NimbusRomNo9L-ReguItal; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;"><em>n</em><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;">but for <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>p </em><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;">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;">they are not the same.</span></span></span></span></span></span></span></span></span></span><br style="font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px;" /></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.extent | 1318 | |
| dc.format.mimetype | application/pdf | |
| dc.language | English | |
| dc.language.iso | en_US | |
| dc.publisher | Vali-e-Asr university of Rafsanjan | en_US |
| dc.relation.ispartof | Wavelet and Linear Algebra | en_US |
| dc.relation.ispartof | موجک و جبر خطی | fa_IR |
| dc.subject | Linear preservers | en_US |
| dc.subject | Matrix majorization | en_US |
| dc.subject | Row stochastic matrix | en_US |
| dc.title | Linear preservers of two-sided matrix majorization | en_US |
| dc.type | Text | en_US |
| dc.type | Research Paper | en_US |
| dc.contributor.department | Department of Mathmatics, Faculty of Mathmatics, Shahid Bahonar University of Kerman,
Kerman, Islamic Republic of Iran | en_US |
| dc.citation.volume | 1 | |
| dc.citation.issue | 1 | |
| dc.citation.spage | 43 | |
| dc.citation.epage | 50 | |
