Pascal matrices and Toeplitz matrices: Relations. Issue 6 (7th September 2020)

• Record Type: Journal Article
• Authors: Tomeo, Venancio; Torrano, Emilio
• Is Part Of: Computational and mathematical methods. Volume 2:Issue 6(2020)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-09-07
• Subjects: bilateral sequences -- binomial transformation -- combinatorial numbers -- moment matrix -- Pascal matrices -- Pascal triangle -- similarity transformation -- Toeplitz matrix; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1119
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract : We extend the concept of Pascal matrix to all matrices with the property that entries are the sum of left and above entries. We have obtained an algebraic relation that allows us to obtain a Toeplitz matrix from a Pascal matrix, and vice versa. This procedure can be applied to any Pascal matrices and any Toeplitz matrices, Hermitian matrices or not, moment matrices or not. The relationship with the difference operator and with the shift operator is also studied.