ON THE INVERSE OF PATTERN MATRICES WITH APPLICATION TO STATISICAL MODELS
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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.
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