Some properties of a class of band matrices
Abstract: Let denote the band matrix, of bandwidth , with the binomial coefficients in the expansion of as the elements in each row and column. Using the fact that the rows of provide the coefficients for the th central difference, a number of properties of are obtained for all positive integers and . These include obtaining explicit formulas for and an upper triangular matrix such that is lower triangular.
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Keywords: Determinants, band matrices, inverse matrices, norms on inverses
Article copyright: © Copyright 1972 American Mathematical Society