Infinite triangular matrices, q-Pascal matrices, and determinantal representations

✍ Scribed by Luis Verde-Star

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 186 KB
• Volume: 434
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2010.08.022

✦ Synopsis

We use basic properties of infinite lower triangular matrices and the connections of Toeplitz matrices with generating-functions to obtain inversion formulas for several types of q-Pascal matrices, determinantal representations for polynomial sequences, and identities involving the q-Gaussian coefficients. We also obtain a fast inversion algorithm for general infinite lower triangular matrices.