VanderLaan Circulant Type Matrices
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, and g-circulant matrices. The nonsingularity of these special matrices is discussed b...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/329329 |
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| author | Hongyan Pan Zhaolin Jiang |
| author_facet | Hongyan Pan Zhaolin Jiang |
| author_sort | Hongyan Pan |
| collection | DOAJ |
| description | 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, and g-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 VanderLaan g-circulant matrix. |
| format | Article |
| id | doaj-art-02bedcf9d1e3451fbd570586e94d2d93 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-02bedcf9d1e3451fbd570586e94d2d932025-02-03T05:44:52ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/329329329329VanderLaan Circulant Type MatricesHongyan Pan0Zhaolin Jiang1Department of Mathematics, Linyi University, Linyi, Shandong 276000, ChinaDepartment of Mathematics, Linyi University, Linyi, Shandong 276000, ChinaCirculant 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, and g-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 VanderLaan g-circulant matrix.http://dx.doi.org/10.1155/2015/329329 |
| spellingShingle | Hongyan Pan Zhaolin Jiang VanderLaan Circulant Type Matrices Abstract and Applied Analysis |
| title | VanderLaan Circulant Type Matrices |
| title_full | VanderLaan Circulant Type Matrices |
| title_fullStr | VanderLaan Circulant Type Matrices |
| title_full_unstemmed | VanderLaan Circulant Type Matrices |
| title_short | VanderLaan Circulant Type Matrices |
| title_sort | vanderlaan circulant type matrices |
| url | http://dx.doi.org/10.1155/2015/329329 |
| work_keys_str_mv | AT hongyanpan vanderlaancirculanttypematrices AT zhaolinjiang vanderlaancirculanttypematrices |