Distribution theory of quadratic forms with matrix argument

Jose A. Diaz-Garcia

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arXiv · 1210.5283

Distribution theory of quadratic forms with matrix argument

Jose A. Diaz-Garcia

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Abstract

This paper proposes the density and characteristic functions of a general matrix quadratic form $\mathbf{X}^{*}\mathbf{AX}$, when $\mathbf{A} = \mathbf{A}^{*}$, $\mathbf{X}$ has a matrix multivariate elliptical distribution and $\mathbf{X}^{*}$ denotes the usual conjugate transpose of $\mathbf{X}$. These results are obtained for real normed division algebras. With particular cases we obtained the density and characteristic functions of matrix quadratic forms for matrix multivariate normal, Pearson type VII, $t$ and Cauchy distributions.

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Jose A. Diaz-Garcia. 2012-10-18. Distribution theory of quadratic forms with matrix argument. https://arxiv.org/abs/1210.5283

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