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


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1 Centre for Mathematical Sciences India, Arunapuram, P.O., Palai, Kerala-686 574, Kerala, India
     

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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.

Keywords

Matrix-Variate Gamma Integral, Matrix-Variate Beta Integrals, Explicit Evaluations, Real and Complex Cases, Partitioned Matrices and Determinants.
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  • T. W. Anderson, An Introduction to Multivariate Statistical Analysis, Wiley, New York, 1971.
  • A.M. Kshirsagar,Multivariate Analysis, Marcel Dekker, New York, 1972.
  • A.M. Mathai, Jacobians of Matrix Transformations and Functions of Matrix Argument, World Scientific Publishing, New York, 1997.
  • M.S. Srivastava and C.G., An Introduction to Multivariate Statistics, North Holland, New York, 1979.

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

Abstract Views: 263  |  PDF Views: 0

Authors

A. M. Mathai
Centre for Mathematical Sciences India, Arunapuram, P.O., Palai, Kerala-686 574, Kerala, India

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.

Keywords


Matrix-Variate Gamma Integral, Matrix-Variate Beta Integrals, Explicit Evaluations, Real and Complex Cases, Partitioned Matrices and Determinants.

References