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Invertibility Of Submatrices Of The Pascal Matrix And Birkhoff Interpolation, Scott N. Kersey

Department of Mathematical Sciences Faculty Publications

The infinite upper triangular Pascal matrix is T = [( j )i] for 0 ≤ i, j. It is easy to see that any leading principle square submatrix is triangular with determinant 1, hence invertible. In this paper, we investigate the invertibility of arbitrary square submatrices Tr, c comprised of rows r = [r0, … , rm ] and columns c = c0 , … , cm[] of T. We show that Tr, c is invertible r ≤ c i.e., ri ≤ ci for i = 0, …, m(), or equivalently, iff all diagonal entries are nonzero. To prove this …