Loading…

Monotonicity, path product matrices, and principal submatrices

It is shown that, if for some m, 2≤m

Saved in:

Bibliographic Details
Published in:	Linear algebra and its applications 2020-05, Vol.593, p.269-275
Main Authors:	Bechtold, B.K., Johnson, C.R.
Format:	Article
Language:	English
Subjects:	Doubly monotone matrices Doubly nonnegative matrices Linear algebra Mathematical analysis Matrix methods Monotone matrices P-matrices Path product matrices Principal submatrices
Citations:	Items that this one cites
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

cited_by
cites	cdi_FETCH-LOGICAL-c320t-9c8961d43f01fa4969e4f4fc29e1c53d8ecd2a9ce7139fb0c64ee3ba76f2d24c3
container_end_page	275
container_issue
container_start_page	269
container_title	Linear algebra and its applications
container_volume	593
creator	Bechtold, B.K. Johnson, C.R.
description	It is shown that, if for some m, 2≤m
doi_str_mv	10.1016/j.laa.2020.02.001
format	article
fullrecord	<record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2438724908</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0024379520300604</els_id><sourcerecordid>2438724908</sourcerecordid><originalsourceid>FETCH-LOGICAL-c320t-9c8961d43f01fa4969e4f4fc29e1c53d8ecd2a9ce7139fb0c64ee3ba76f2d24c3</originalsourceid><addsrcrecordid>eNp9kM1LAzEQxYMoWKt_gLcFr9118tHdDYIgpX5AxYueQzpJMEu7W5Os0P_elOrV08Cb92YeP0KuKVQUaH3bVRutKwYMKmAVAD0hE9o2vKTtvD4lEwAmSt7I-Tm5iLEDANEAm5D716Ef0tB79Gk_K3Y6fRa7MJgRU7HVKXi0cVbo3mTV9-h3elPEcf23uiRnTm-ivfqdU_LxuHxfPJert6eXxcOqRM4glRJbWVMjuAPqtJC1tMIJh0xainNuWouGaYm2oVy6NWAtrOVr3dSOGSaQT8nN8W7u9jXamFQ3jKHPLxUTvG2YkNBmFz26MAwxButULr3VYa8oqAMm1amMSR0wKWAqY8qZu2PG5vrf3gYV0dserfHBYlJm8P-kfwB4OnAH</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2438724908</pqid></control><display><type>article</type><title>Monotonicity, path product matrices, and principal submatrices</title><source>ScienceDirect Journals</source><creator>Bechtold, B.K. ; Johnson, C.R.</creator><creatorcontrib>Bechtold, B.K. ; Johnson, C.R.</creatorcontrib><description>It is shown that, if for some m, 2≤m<n all principal submatrices of an n-by-n P-matrix A are monotone, then A is monotone, generalizing a known result that also assumed symmetry. It is also shown that the P-matrix assumption cannot be entirely eliminated. However, in addition, A is doubly monotone (n=m−1 above, without the P-matrix assumption) if and only if A−1 is invertible path product. It was known that inverse M-matrices are path product (they are more than doubly monotone). But (invertible) path product matrices are more general, and this is the first full and functional characterization of them. Several examples are given to illustrate the results and their generality.</description><identifier>ISSN: 0024-3795</identifier><identifier>EISSN: 1873-1856</identifier><identifier>DOI: 10.1016/j.laa.2020.02.001</identifier><language>eng</language><publisher>Amsterdam: Elsevier Inc</publisher><subject>Doubly monotone matrices ; Doubly nonnegative matrices ; Linear algebra ; Mathematical analysis ; Matrix methods ; Monotone matrices ; P-matrices ; Path product matrices ; Principal submatrices</subject><ispartof>Linear algebra and its applications, 2020-05, Vol.593, p.269-275</ispartof><rights>2020 Elsevier Inc.</rights><rights>Copyright American Elsevier Company, Inc. May 15, 2020</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c320t-9c8961d43f01fa4969e4f4fc29e1c53d8ecd2a9ce7139fb0c64ee3ba76f2d24c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27923,27924</link.rule.ids></links><search><creatorcontrib>Bechtold, B.K.</creatorcontrib><creatorcontrib>Johnson, C.R.</creatorcontrib><title>Monotonicity, path product matrices, and principal submatrices</title><title>Linear algebra and its applications</title><description>It is shown that, if for some m, 2≤m<n all principal submatrices of an n-by-n P-matrix A are monotone, then A is monotone, generalizing a known result that also assumed symmetry. It is also shown that the P-matrix assumption cannot be entirely eliminated. However, in addition, A is doubly monotone (n=m−1 above, without the P-matrix assumption) if and only if A−1 is invertible path product. It was known that inverse M-matrices are path product (they are more than doubly monotone). But (invertible) path product matrices are more general, and this is the first full and functional characterization of them. Several examples are given to illustrate the results and their generality.</description><subject>Doubly monotone matrices</subject><subject>Doubly nonnegative matrices</subject><subject>Linear algebra</subject><subject>Mathematical analysis</subject><subject>Matrix methods</subject><subject>Monotone matrices</subject><subject>P-matrices</subject><subject>Path product matrices</subject><subject>Principal submatrices</subject><issn>0024-3795</issn><issn>1873-1856</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kM1LAzEQxYMoWKt_gLcFr9118tHdDYIgpX5AxYueQzpJMEu7W5Os0P_elOrV08Cb92YeP0KuKVQUaH3bVRutKwYMKmAVAD0hE9o2vKTtvD4lEwAmSt7I-Tm5iLEDANEAm5D716Ef0tB79Gk_K3Y6fRa7MJgRU7HVKXi0cVbo3mTV9-h3elPEcf23uiRnTm-ivfqdU_LxuHxfPJert6eXxcOqRM4glRJbWVMjuAPqtJC1tMIJh0xainNuWouGaYm2oVy6NWAtrOVr3dSOGSaQT8nN8W7u9jXamFQ3jKHPLxUTvG2YkNBmFz26MAwxButULr3VYa8oqAMm1amMSR0wKWAqY8qZu2PG5vrf3gYV0dserfHBYlJm8P-kfwB4OnAH</recordid><startdate>20200515</startdate><enddate>20200515</enddate><creator>Bechtold, B.K.</creator><creator>Johnson, C.R.</creator><general>Elsevier Inc</general><general>American Elsevier Company, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20200515</creationdate><title>Monotonicity, path product matrices, and principal submatrices</title><author>Bechtold, B.K. ; Johnson, C.R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c320t-9c8961d43f01fa4969e4f4fc29e1c53d8ecd2a9ce7139fb0c64ee3ba76f2d24c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Doubly monotone matrices</topic><topic>Doubly nonnegative matrices</topic><topic>Linear algebra</topic><topic>Mathematical analysis</topic><topic>Matrix methods</topic><topic>Monotone matrices</topic><topic>P-matrices</topic><topic>Path product matrices</topic><topic>Principal submatrices</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bechtold, B.K.</creatorcontrib><creatorcontrib>Johnson, C.R.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Linear algebra and its applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bechtold, B.K.</au><au>Johnson, C.R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Monotonicity, path product matrices, and principal submatrices</atitle><jtitle>Linear algebra and its applications</jtitle><date>2020-05-15</date><risdate>2020</risdate><volume>593</volume><spage>269</spage><epage>275</epage><pages>269-275</pages><issn>0024-3795</issn><eissn>1873-1856</eissn><abstract>It is shown that, if for some m, 2≤m<n all principal submatrices of an n-by-n P-matrix A are monotone, then A is monotone, generalizing a known result that also assumed symmetry. It is also shown that the P-matrix assumption cannot be entirely eliminated. However, in addition, A is doubly monotone (n=m−1 above, without the P-matrix assumption) if and only if A−1 is invertible path product. It was known that inverse M-matrices are path product (they are more than doubly monotone). But (invertible) path product matrices are more general, and this is the first full and functional characterization of them. Several examples are given to illustrate the results and their generality.</abstract><cop>Amsterdam</cop><pub>Elsevier Inc</pub><doi>10.1016/j.laa.2020.02.001</doi><tpages>7</tpages><oa>free_for_read</oa></addata></record>
fulltext	fulltext
identifier	ISSN: 0024-3795
ispartof	Linear algebra and its applications, 2020-05, Vol.593, p.269-275
issn	0024-3795 1873-1856
language	eng
recordid	cdi_proquest_journals_2438724908
source	ScienceDirect Journals
subjects	Doubly monotone matrices Doubly nonnegative matrices Linear algebra Mathematical analysis Matrix methods Monotone matrices P-matrices Path product matrices Principal submatrices
title	Monotonicity, path product matrices, and principal submatrices
url	http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-08T16%3A49%3A21IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Monotonicity,%20path%20product%20matrices,%20and%20principal%20submatrices&rft.jtitle=Linear%20algebra%20and%20its%20applications&rft.au=Bechtold,%20B.K.&rft.date=2020-05-15&rft.volume=593&rft.spage=269&rft.epage=275&rft.pages=269-275&rft.issn=0024-3795&rft.eissn=1873-1856&rft_id=info:doi/10.1016/j.laa.2020.02.001&rft_dat=%3Cproquest_cross%3E2438724908%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c320t-9c8961d43f01fa4969e4f4fc29e1c53d8ecd2a9ce7139fb0c64ee3ba76f2d24c3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2438724908&rft_id=info:pmid/&rfr_iscdi=true