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Matrix Anal. Appl."],"published-print":{"date-parts":[[2024,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Hypergraphs and tensors extend classic graph and matrix theories to account for multiway relationships, which are ubiquitous in engineering, biological, and social systems. While the Kronecker product is a potent tool for analyzing the coupling of systems in a graph or matrix context, its utility in studying multiway interactions, such as those represented by tensors and hypergraphs, remains elusive. In this article, we present a comprehensive exploration of algebraic, structural, and spectral properties of the tensor Kronecker product. We express Tucker and tensor train decompositions and various tensor eigenvalues in terms of the tensor Kronecker product. Additionally, we utilize the tensor Kronecker product to form Kronecker hypergraphs, which are tensor-based hypergraph products, and investigate the structure and stability of polynomial dynamics on Kronecker hypergraphs. Finally, we provide numerical examples to demonstrate the utility of the tensor Kronecker product in computing Z-eigenvalues, performing various tensor decompositions, and determining the stability of polynomial systems.<\/jats:p>","DOI":"10.1137\/23m1592547","type":"journal-article","created":{"date-parts":[[2024,9,3]],"date-time":"2024-09-03T09:07:26Z","timestamp":1725354446000},"page":"1621-1642","source":"Crossref","is-referenced-by-count":13,"title":["Kronecker Product of Tensors and Hypergraphs: Structure and Dynamics"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8763-3200","authenticated-orcid":true,"given":"Joshua","family":"Pickard","sequence":"first","affiliation":[{"name":"Department of Computational Medicine & Bioinformatics, University of Michigan, Ann Arbor, MI 48109 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2310-0074","authenticated-orcid":true,"given":"Can","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Data Science and Society and Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cooper","family":"Stansbury","sequence":"additional","affiliation":[{"name":"Department of Computational Medicine & Bioinformatics, University of Michigan, Ann Arbor, MI 48109 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6409-5139","authenticated-orcid":true,"given":"Amit","family":"Surana","sequence":"additional","affiliation":[{"name":"Raytheon Technologies Research Center, East Hartford, CT 06108 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anthony M.","family":"Bloch","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Indika","family":"Rajapakse","sequence":"additional","affiliation":[{"name":"Department of Computational Medicine & Bioinformatics, Medical School and Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,9,3]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","unstructured":"L. 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