Explicit Expression for Arbitrary Positive Integer Powers of Special Sparse Matrices
Sparse matrices appear frequently in mathematical models. In this paper, we firstly present a general expression for the entries of the r th r∈ℕ power of a certain n-square sparse matrix, in terms of the Chebyshev polynomials of the second kind. Secondly, we present a method for integer positive pow...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1076545 |
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| author | Mohammad Beiranvand Mojtaba Ghasemi Kamalvand |
| author_facet | Mohammad Beiranvand Mojtaba Ghasemi Kamalvand |
| author_sort | Mohammad Beiranvand |
| collection | DOAJ |
| description | Sparse matrices appear frequently in mathematical models. In this paper, we firstly present a general expression for the entries of the r th r∈ℕ power of a certain n-square sparse matrix, in terms of the Chebyshev polynomials of the second kind. Secondly, we present a method for integer positive powers of the skew matrix corresponding to these sparse matrices. This method will be inspiring to calculate the positive integer powers of the similar matrices. Finally, we present some examples to illustrate our results. Also, we give maple 18 procedures in order to verify our calculations. |
| format | Article |
| id | doaj-art-c815e13ac89f40f3b9e4273e2b6b7285 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c815e13ac89f40f3b9e4273e2b6b72852025-02-03T00:59:38ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/1076545Explicit Expression for Arbitrary Positive Integer Powers of Special Sparse MatricesMohammad Beiranvand0Mojtaba Ghasemi Kamalvand1Department of MathematicsDepartment of MathematicsSparse matrices appear frequently in mathematical models. In this paper, we firstly present a general expression for the entries of the r th r∈ℕ power of a certain n-square sparse matrix, in terms of the Chebyshev polynomials of the second kind. Secondly, we present a method for integer positive powers of the skew matrix corresponding to these sparse matrices. This method will be inspiring to calculate the positive integer powers of the similar matrices. Finally, we present some examples to illustrate our results. Also, we give maple 18 procedures in order to verify our calculations.http://dx.doi.org/10.1155/2022/1076545 |
| spellingShingle | Mohammad Beiranvand Mojtaba Ghasemi Kamalvand Explicit Expression for Arbitrary Positive Integer Powers of Special Sparse Matrices Journal of Mathematics |
| title | Explicit Expression for Arbitrary Positive Integer Powers of Special Sparse Matrices |
| title_full | Explicit Expression for Arbitrary Positive Integer Powers of Special Sparse Matrices |
| title_fullStr | Explicit Expression for Arbitrary Positive Integer Powers of Special Sparse Matrices |
| title_full_unstemmed | Explicit Expression for Arbitrary Positive Integer Powers of Special Sparse Matrices |
| title_short | Explicit Expression for Arbitrary Positive Integer Powers of Special Sparse Matrices |
| title_sort | explicit expression for arbitrary positive integer powers of special sparse matrices |
| url | http://dx.doi.org/10.1155/2022/1076545 |
| work_keys_str_mv | AT mohammadbeiranvand explicitexpressionforarbitrarypositiveintegerpowersofspecialsparsematrices AT mojtabaghasemikamalvand explicitexpressionforarbitrarypositiveintegerpowersofspecialsparsematrices |