Affiliation:
1. Department of Mathematics, Linyi University, Linyi, Shandong 276000, China
Abstract
Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant, left circulant, andg-circulant matrices. The nonsingularity of these special matrices is discussed by the surprising properties of VanderLaan numbers. The exact determinants of VanderLaan circulant type matrices are given by structuring transformation matrices, determinants of well-known tridiagonal matrices, and tridiagonal-like matrices. The explicit inverse matrices of these special matrices are obtained by structuring transformation matrices, inverses of known tridiagonal matrices, and quasi-tridiagonal matrices. Three kinds of norms and lower bound for the spread of VanderLaan circulant and left circulant matrix are given separately. And we gain the spectral norm of VanderLaang-circulant matrix.
Funder
Development Project of Science & Technology of Shandong Province
Subject
Applied Mathematics,Analysis
Cited by
2 articles.
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1. The Fibonacci–Circulant Sequences and Their Applications;Iranian Journal of Science and Technology, Transactions A: Science;2017-11-01
2. The adjacency-Jacobsthal-circulant numbers;AIP Conference Proceedings;2017