An umbral approach to find q-analogues of matrix formulas

• A general introduction is given to the logarithmic q-analogue formulation of mathematical expressions with a special focus on its use for matrix calculations. The fundamental definitions relevant to q-analogues of mathematical objects are given and form the basis for matrix formulations in the paper. The umbral approach is used to find q-analogues of significant matrices. Finally, as an explicit example, a new formula for q-Cauchy-Vandermonde determinant containing matrix elements equal to q-numbers introduced by Ward is proved by using a new type of q-Stirling numbers together with Lagrange interpolation in Z(q).

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

NWA q-addition

Matrix power series

q-Cauchy-Vandermonde determinant

q-Stirling numbers

q-Exponential function

Ring

LU factorization

Publication and Content Type

ref (subject category)

art (subject category)