Infinite matrix products and the representation of the matrix gamma function. (English) Zbl 1383.15026

Summary: We introduce infinite matrix products including some of their main properties and convergence results. We apply them in order to extend to the matrix scenario the definition of the scalar gamma function given by an infinite product due to Weierstrass. A limit representation of the matrix gamma function is also provided.


15A99 Basic linear algebra
33B15 Gamma, beta and polygamma functions
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