{"title":"Fibonacci-Sylvester-Kac矩阵的特征多项式、行列式和逆","authors":"Zhaolin Jiang, Yanpeng Zheng, Tianzi Li","doi":"10.1515/spma-2021-0145","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we consider a new Sylvester-Kac matrix, i.e., Fibonacci-Sylvester-Kac matrix. We discuss the eigenvalues, eigenvectors and characteristic polynomial of this matrix in two categories based on whether the Fibonacci-Sylvester-Kac matrix order is odd or even. Besides, we also give the explicit formulas for its determinant and inverse.","PeriodicalId":43276,"journal":{"name":"Special Matrices","volume":"10 1","pages":"40 - 46"},"PeriodicalIF":0.8000,"publicationDate":"2021-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Characteristic polynomial, determinant and inverse of a Fibonacci-Sylvester-Kac matrix\",\"authors\":\"Zhaolin Jiang, Yanpeng Zheng, Tianzi Li\",\"doi\":\"10.1515/spma-2021-0145\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, we consider a new Sylvester-Kac matrix, i.e., Fibonacci-Sylvester-Kac matrix. We discuss the eigenvalues, eigenvectors and characteristic polynomial of this matrix in two categories based on whether the Fibonacci-Sylvester-Kac matrix order is odd or even. Besides, we also give the explicit formulas for its determinant and inverse.\",\"PeriodicalId\":43276,\"journal\":{\"name\":\"Special Matrices\",\"volume\":\"10 1\",\"pages\":\"40 - 46\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-08-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Special Matrices\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/spma-2021-0145\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Special Matrices","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/spma-2021-0145","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Characteristic polynomial, determinant and inverse of a Fibonacci-Sylvester-Kac matrix
Abstract In this paper, we consider a new Sylvester-Kac matrix, i.e., Fibonacci-Sylvester-Kac matrix. We discuss the eigenvalues, eigenvectors and characteristic polynomial of this matrix in two categories based on whether the Fibonacci-Sylvester-Kac matrix order is odd or even. Besides, we also give the explicit formulas for its determinant and inverse.
期刊介绍：
Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.
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