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The density of the inverse and pseudo-inverse of a random matrix

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  • Olkin, Ingram

Abstract

Given an absolutely continuous density of a random matrix X, we study the density of the inverse when X is a p x p symmetric, triangular and arbitrary matrix, and the pseudo-inverse when X is rectangular. In the latter case we provide alternative proofs to that of Zhang (1985), who first obtained this density.

Suggested Citation

  • Olkin, Ingram, 1998. "The density of the inverse and pseudo-inverse of a random matrix," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 131-135, June.
    • Handle: RePEc:eee:stapro:v:38:y:1998:i:2:p:131-135
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    Cited by:

    1. Hisayuki Tsukuma & Tatsuya Kubokawa, 2014. "Estimation and Prediction Intervals in Transformed Linear Mixed Models," CIRJE F-Series CIRJE-F-930, CIRJE, Faculty of Economics, University of Tokyo.
    2. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2015. "Estimation of the mean vector in a singular multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 245-258.

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