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.

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 12)

Pages:

1-13

DOI:

10.18052/www.scipress.com/BMSA.12.1

Citation:

R. Purushothaman Nair "Non-Unit Bidiagonal Matrices for Factorization of Vandermonde Matrices", Bulletin of Mathematical Sciences and Applications, Vol. 12, pp. 1-13, 2015

Online since:

May 2015

Authors:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License