Factorizations of Matrices With Recursive Entries and Related Topics
Abstract
This article examines matrices whose entries are determined by recursive relations of the form $A_{i, j} = x A_{i, j-1} + y A_{i-1, j-1} + z A_{i-1, j}$, where $x, y, z$ are constants, and the initial conditions are defined along the first row and column. We present a general decomposition for such matrices and show that many of the known decompositions are particular cases of this more general decomposition. Additionally, we provide a decomposition of these matrices into Pascal-like matrices and a basic Toeplitz matrix.
Fields of Study & Subjects
Matrix Theory and Algorithms
Advanced Combinatorial Mathematics
Mathematical functions and polynomials
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 6 February 2026
- Language
- EN
- Document type
- Preprint