A non-unit bidiagonal matrix and its inverse with simple structures are introduced. These matrices can be constructed easily using the entries of a given non-zero vector without any computations among the entries. The matrix transforms the given vector to a column of the identity matrix. The given vector can be computed back without any round off error using the inverse matrix. Since a Vandermonde matrix can also be constructed using given n quantities, it is established in this paper that Vandermonde matrices can be factorized in a simple way by applying these bidiagonal matrices. Also it is demonstrated that factors of Vandermonde and inverse Vandermonde matrices can be conveniently presented using the matrices introduced here.
Bulletin of Mathematical Sciences and Applications (Volume 12)
R. Purushothaman Nair "Non-Unit Bidiagonal Matrices for Factorization of Vandermonde Matrices", Bulletin of Mathematical Sciences and Applications, Vol. 12, pp. 1-13, 2015