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Three results in connection with inverse matrices. (English) Zbl 0562.15003
i. The Moore-Penrose solution of an arbitrary system of linear equations is a convex combination of the solutions of all uniquely solvable partial systems. ii. For a determinant appearing in an explicit formula of D. S. Meek [ibid. 49, 117-129 (1983; Zbl 0505.15005)] concerning the elements of the inverse of a Toeplitz band matrix the asymptotic representation is established under general conditions. iii. For the limit case of an explicit formula of W. D. Hoskins and P. J. Ponzo [Math. Comput. 26, 393-400 (1972; Zbl 0248.15008)] concerning the elements of the inverse of a Toeplitz band matrix with special binomial coefficients there is given a modification and generalization. In the last two cases there are used methods from the discrete operational calculus.

15A09 Theory of matrix inversion and generalized inverses
44A55 Discrete operational calculus
Full Text: DOI
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