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Explicit form of determinants and inverse matrices of Tribonacci r-circulant type matrices

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Abstract

The determinants and inverses of Tribonacci r-circulant type matrices are discussed in the paper. Firstly, Tribonacci r-circulant type matrices are defined. In addition, we show the invertibility of the Tribonacci r-circulant matrix and present the determinant and the inverse matrix based on constructing the transformation matrices. By utilizing the relation between r-circulant and r-left circulant, the invertibility of the Tribonacci r-left circulant matrix are also discussed. Finally, the determinants and the inverse matrices of the these matrices are given, respectively.

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Acknowledgements

This work was supported by the GRRC program of Gyeonggi Province [(GRRC SUWON 2016-B3), Development of cloud Computing-based Intelligent Video Security Surveillance System with Active Tracking Technology]. Their support is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Information and Telecommunications Engineering, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, Korea

    Kicheon Hong

  2. College of Informatics, Linyi University, Linyi, Shandong, China

    Xiaoyu Jiang

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  1. Xiaoyu Jiang
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  2. Kicheon Hong
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Correspondence to Kicheon Hong.

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Jiang, X., Hong, K. Explicit form of determinants and inverse matrices of Tribonacci r-circulant type matrices. J Math Chem 56, 1234–1249 (2018). https://doi.org/10.1007/s10910-017-0843-8

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  • DOI: https://doi.org/10.1007/s10910-017-0843-8

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