ON THE INVERSE OF PATTERN MATRICES WITH APPLICATION TO STATISICAL MODELS

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 B_n , 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