An umbral approach to find \(q\)-analogues of matrix formulas

DOI10.1016/j.laa.2013.03.018zbMath1305.15039OpenAlexW2047686223MaRDI QIDQ389581

Thomas Ernst

Publication date: 21 January 2014

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2013.03.018

zbMATH Keywords

ringLU factorizationmatrix power series\(q\)-Cauchy-Vandermonde determinant\(q\)-exponential function\(q\)-Stirling numbersNWA \(q\)-addition

Mathematics Subject Classification ID

Umbral calculus (05A40) Bell and Stirling numbers (11B73) Determinants, permanents, traces, other special matrix functions (15A15) Matrix equations and identities (15A24) Eigenvalues, singular values, and eigenvectors (15A18) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Basic hypergeometric functions (33D99)

Related Items

Further results on \(q\)-Lie groups, \(q\)-Lie algebras and \(q\)-homogeneous spaces ⋮ On ordinary, linear \(q\)-difference equations, with applications to \(q\)-Sato theory ⋮ Factorizations for \(q\)-Pascal matrices of two variables ⋮ On the \(q\)-exponential of matrix \(q\)-Lie algebras ⋮ \(q\)-Pascal and \(q\)-Wronskian matrices with implications to \(q\)-Appell polynomials ⋮ On several \(q\)-special matrices, including the \(q\)-Bernoulli and \(q\)-Euler matrices

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