ON THE INVERSE OF PATTERN MATRICES WITH APPLICATION TO STATISICAL MODELS

  • Hiba Hani Abdullah

Abstract

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.


http://dx.doi.org/10.25130/tjps.23.2018.140


 


 

Published
Aug 8, 2018
How to Cite
ABDULLAH, Hiba Hani. ON THE INVERSE OF PATTERN MATRICES WITH APPLICATION TO STATISICAL MODELS. Tikrit Journal of Pure Science, [S.l.], v. 23, n. 8, p. 118-121, aug. 2018. ISSN 2415-1726. Available at: <http://tjps.tu.edu.iq/index.php/j/article/view/160>. Date accessed: 08 dec. 2021.
Section
Articles