Decompositions of a matrix by means of its dual matrices with applications

We introduce the notion of dual matrices of an infinite matrix A, which are defined by the dual sequences of the rows of A and naturally connected to the Pascal matrix P=[(ij)](i,j=0,1,2,…). We present the Cholesky decomposition of the symmetric Pascal matrix by means of its dual matrix. Decompositions of a Vandermonde matrix are used to obtain variants of the Lagrange interpolation polynomial of degree ≤n that passes through the n+1 points (i,qi) for i=0,1,…,n.