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- W1567292582 abstract "The infinite upper triangular Pascal matrix is $T = [binom{j}{i}]$ for $0leq i,j$. 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 $T_{r,c}$ comprised of rows $r=[r_0,ldots,r_m]$ and columns $c=[c_0,ldots,c_m]$ of $T$. We show that $T_{r,c}$ is invertible iff $r leq c$ (i.e., $r_i leq c_i$ for $i=0, ldots, m$), or equivalently, iff all diagonal entries are nonzero. To prove this result we establish a connection between the invertibility of these submatrices and polynomial interpolation. In particular, we apply the theory of Birkhoff interpolation and polya{} systems." @default.
- W1567292582 created "2016-06-24" @default.
- W1567292582 creator A5072308743 @default.
- W1567292582 date "2013-03-25" @default.
- W1567292582 modified "2023-09-27" @default.
- W1567292582 title "Invertibility of Submatrices of Pascal's Matrix and Birkhoff Interpolation" @default.
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