ON THE INVERSE OF PATTERN MATRICES WITH APPLICATION TO STATISICAL MODELS
In this study the inverse of two patterned matrices has been investigated. First, for a Toeplitz-type matrix, it is proved that the exact number of independent cofactors is (n +2)/4 when n is even number and when n is an odd. Second, when the matrix is reduced to a Jacobi-type matrix Bn , two equi...
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| Language: | English |
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Tikrit University
2018-08-01
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| Series: | Tikrit Journal of Pure Science |
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| Online Access: | https://tjpsj.org/index.php/tjps/article/view/554 |
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| author | Hiba Hani Abdullah |
| author_facet | Hiba Hani Abdullah |
| author_sort | Hiba Hani Abdullah |
| collection | DOAJ |
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In this study the inverse of two patterned matrices has been investigated. First, for a Toeplitz-type matrix, it is proved that the exact number of independent cofactors is (n +2)/4 when n is even number and when n is an odd. Second, when the matrix is reduced to a Jacobi-type matrix Bn , two equivalent formulae for its determinant are obtained, one of which in terms of the eigen values. Moreover, it is proved that the independent cofactors of are explicitly expressed as a product of the determinants of and . So, the problem of finding the exact inverse of is reduced to that one of finding the determinants of , i = 1, 2, …, n.
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| format | Article |
| id | doaj-art-aeafaf2d634449dcbbe0a161a5c74d6a |
| institution | OA Journals |
| issn | 1813-1662 2415-1726 |
| language | English |
| publishDate | 2018-08-01 |
| publisher | Tikrit University |
| record_format | Article |
| series | Tikrit Journal of Pure Science |
| spelling | doaj-art-aeafaf2d634449dcbbe0a161a5c74d6a2025-08-20T02:36:59ZengTikrit UniversityTikrit Journal of Pure Science1813-16622415-17262018-08-0123810.25130/tjps.v23i8.554ON THE INVERSE OF PATTERN MATRICES WITH APPLICATION TO STATISICAL MODELSHiba Hani Abdullah In this study the inverse of two patterned matrices has been investigated. First, for a Toeplitz-type matrix, it is proved that the exact number of independent cofactors is (n +2)/4 when n is even number and when n is an odd. Second, when the matrix is reduced to a Jacobi-type matrix Bn , two equivalent formulae for its determinant are obtained, one of which in terms of the eigen values. Moreover, it is proved that the independent cofactors of are explicitly expressed as a product of the determinants of and . So, the problem of finding the exact inverse of is reduced to that one of finding the determinants of , i = 1, 2, …, n. https://tjpsj.org/index.php/tjps/article/view/554patterned matricesToeplitz-type matrixJacobi-type matrixEigen values |
| spellingShingle | Hiba Hani Abdullah ON THE INVERSE OF PATTERN MATRICES WITH APPLICATION TO STATISICAL MODELS Tikrit Journal of Pure Science patterned matrices Toeplitz-type matrix Jacobi-type matrix Eigen values |
| title | ON THE INVERSE OF PATTERN MATRICES WITH APPLICATION TO STATISICAL MODELS |
| title_full | ON THE INVERSE OF PATTERN MATRICES WITH APPLICATION TO STATISICAL MODELS |
| title_fullStr | ON THE INVERSE OF PATTERN MATRICES WITH APPLICATION TO STATISICAL MODELS |
| title_full_unstemmed | ON THE INVERSE OF PATTERN MATRICES WITH APPLICATION TO STATISICAL MODELS |
| title_short | ON THE INVERSE OF PATTERN MATRICES WITH APPLICATION TO STATISICAL MODELS |
| title_sort | on the inverse of pattern matrices with application to statisical models |
| topic | patterned matrices Toeplitz-type matrix Jacobi-type matrix Eigen values |
| url | https://tjpsj.org/index.php/tjps/article/view/554 |
| work_keys_str_mv | AT hibahaniabdullah ontheinverseofpatternmatriceswithapplicationtostatisicalmodels |