Products of multidimensional matrices, stochastic matrices, and permanents
In this paper we consider four basic multidimensional matrix operations (outer product, Kronecker product, contraction, and projection) and two derivative operations (dot and circle products). We start with the interrelations between these operations and deduce some of their algebraic properties. Ne...
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creator | Taranenko, Anna A |
description | In this paper we consider four basic multidimensional matrix operations
(outer product, Kronecker product, contraction, and projection) and two
derivative operations (dot and circle products). We start with the
interrelations between these operations and deduce some of their algebraic
properties. Next, we study their action on $k$-stochastic matrices. At last, we
prove several relations on the permanents of products of multidimensional
matrices. In particular, we obtain that the permanent of the dot product of
nonnegative multidimensional matrices is not less than the product of their
permanents and show that inequalities on the Kronecker product of nonnegative
2-dimensional matrices cannot be extended to the multidimensional case. |
doi_str_mv | 10.48550/arxiv.2303.17278 |
format | Article |
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(outer product, Kronecker product, contraction, and projection) and two
derivative operations (dot and circle products). We start with the
interrelations between these operations and deduce some of their algebraic
properties. Next, we study their action on $k$-stochastic matrices. At last, we
prove several relations on the permanents of products of multidimensional
matrices. In particular, we obtain that the permanent of the dot product of
nonnegative multidimensional matrices is not less than the product of their
permanents and show that inequalities on the Kronecker product of nonnegative
2-dimensional matrices cannot be extended to the multidimensional case.</description><identifier>DOI: 10.48550/arxiv.2303.17278</identifier><language>eng</language><subject>Mathematics - Combinatorics</subject><creationdate>2023-03</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2303.17278$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2303.17278$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Taranenko, Anna A</creatorcontrib><title>Products of multidimensional matrices, stochastic matrices, and permanents</title><description>In this paper we consider four basic multidimensional matrix operations
(outer product, Kronecker product, contraction, and projection) and two
derivative operations (dot and circle products). We start with the
interrelations between these operations and deduce some of their algebraic
properties. Next, we study their action on $k$-stochastic matrices. At last, we
prove several relations on the permanents of products of multidimensional
matrices. In particular, we obtain that the permanent of the dot product of
nonnegative multidimensional matrices is not less than the product of their
permanents and show that inequalities on the Kronecker product of nonnegative
2-dimensional matrices cannot be extended to the multidimensional case.</description><subject>Mathematics - Combinatorics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNpNz81KxDAUhuFsXMjoBbgyF2Br2pz2pEsZ_GVAF7MvJ38YaNIhyYjevTi6cPXBu_jgYeyqEy2oYRC3lD_DR9tLIdsOe1Tn7OUtr_ZoauGr5_G41GBDdKmENdHCI9UcjCs3vNTVvFOpwfyLlCw_uBwpuVTLBTvztBR3-bcbtn-432-fmt3r4_P2btfQiKqxzoKDHgc9aonKkkcHtrOTQ6PU5ECj6RAIEbweVa_QAHrUQgmQgJPcsOvf2xNmPuQQKX_NP6j5hJLfCkBITQ</recordid><startdate>20230330</startdate><enddate>20230330</enddate><creator>Taranenko, Anna A</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20230330</creationdate><title>Products of multidimensional matrices, stochastic matrices, and permanents</title><author>Taranenko, Anna A</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a678-ded4e4275b6b378daf7e4d1d9e7c889e4b7c174a774fb68287c47f7b080434793</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Mathematics - Combinatorics</topic><toplevel>online_resources</toplevel><creatorcontrib>Taranenko, Anna A</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Taranenko, Anna A</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Products of multidimensional matrices, stochastic matrices, and permanents</atitle><date>2023-03-30</date><risdate>2023</risdate><abstract>In this paper we consider four basic multidimensional matrix operations
(outer product, Kronecker product, contraction, and projection) and two
derivative operations (dot and circle products). We start with the
interrelations between these operations and deduce some of their algebraic
properties. Next, we study their action on $k$-stochastic matrices. At last, we
prove several relations on the permanents of products of multidimensional
matrices. In particular, we obtain that the permanent of the dot product of
nonnegative multidimensional matrices is not less than the product of their
permanents and show that inequalities on the Kronecker product of nonnegative
2-dimensional matrices cannot be extended to the multidimensional case.</abstract><doi>10.48550/arxiv.2303.17278</doi><oa>free_for_read</oa></addata></record> |
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subjects | Mathematics - Combinatorics |
title | Products of multidimensional matrices, stochastic matrices, and permanents |
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