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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Tikrit University
2018-08-01
|
| Series: | Tikrit Journal of Pure Science |
| Subjects: | |
| Online Access: | https://tjpsj.org/index.php/tjps/article/view/554 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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.
|
|---|---|
| ISSN: | 1813-1662 2415-1726 |