{"title":"Mutual incidence matrix of two balanced incomplete block designs","authors":"Alexander Shramchenko, Vasilisa Shramchenko","doi":"arxiv-2312.03937","DOIUrl":null,"url":null,"abstract":"We propose to consider a mutual incidence matrix $M$ of two balanced\nincomplete block designs built on the same finite set. In the simplest case,\nthis matrix reduces to the standard incidence matrix of one block design. We\nfind all eigenvalues of the matrices $MM^T$ and $M^TM$ and their eigenspaces.","PeriodicalId":501407,"journal":{"name":"arXiv - MATH - Combinatorics","volume":"25 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2312.03937","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We propose to consider a mutual incidence matrix $M$ of two balanced
incomplete block designs built on the same finite set. In the simplest case,
this matrix reduces to the standard incidence matrix of one block design. We
find all eigenvalues of the matrices $MM^T$ and $M^TM$ and their eigenspaces.
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