The factorization of block matrices with generalized geometric progression rows

AbstractGeneralized geometric progression (GP) block matrices are introduced, and it is shown that such matrices can be factored as the product of one lower triangular matrix and several upper triangular reduced Pascal matrices, P̄k[x], which were introduced by Cheon and Kim. The determinant formula for any (GP) block matrix follows readily from this factorization. This LU factorization and determinant formula are a generalization of results presented by Yang and Leida. As direct applications of the new results, we rederive factorizations of the extended generalized symmetric Pascal matrix, introduced by Zhang and Liu, and the Vandermonde matrix. In addition, determinants of three types of generalized Vandermonde matrices are immediate consequences of our main theorem