Explicit Evaluations of Matrix-variate Gamma and Beta Integrals in the Real and Complex Cases

zbMATH Open1322.15016arXiv1409.7561MaRDI QIDQ5263374

Arakaparampil M. Mathai

Publication date: 16 July 2015

Abstract: Matrix transformations in terms of triangular matrices is the easiest method of evaluating matrix-variate gamma and beta integrals in the real and complex cases. Here we give several procedures of explicit evaluation of gamma and beta integrals in the general real and complex situations. The procedure also reveals the structure of these matrix-variate integrals. Apart from the evaluation of matrix-variate gamma and beta integrals, the procedure can also be applied to evaluate such integrals explicitly in similar situations. Various methods described here will be useful to those who are working on integrals involving real-valued scalar functions of matrix argument in general and gamma and beta integrals in particular.

Full work available at URL: https://arxiv.org/abs/1409.7561

zbMATH Keywords

complex casereal caseexplicit evaluationsmatrix-variate beta integralsmatrix-variate gamma integralpartitioned matrices and determinants

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Gamma, beta and polygamma functions (33B15) Hermitian, skew-Hermitian, and related matrices (15B57) Other functions defined by series and integrals (33E20)

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