On the distribution of the maximum latent root of a positive definite symmetric random matrix

  • Takesi Hayakawa


In this paper, we consider the distribution of the maximum latent root of a certain positive definite symmetric random matrix. For this purpose, we give a useful transformation of a symmetric matrix and calculate its Jacobian. We also give some useful expansion formulas for zonal polynomials (A. T. James [3]).

Recently Sugiyama [7] and Sugiyama and Hukutomi [8] gave the density functions of maximum latent roots of a central Wishart matrix when the covariance matrix Σ=I, and of a multivariate Beta matrix and a multivariateF-matrix in the central case.

Here we derive the density functions of maximum latent roots of a multivariate non-central Beta matrix, a non-central Wishart matrix and a multivariate central quadratic form with the covariance matrix Σ, and we also derive the density function of maximum canonical correlation coefficient. The notations in this paper are due to A. T. James [4] and A. G. Constantine [1].


Density Function Covariance Matrix Latent Root Expansion Formula Joint Density Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© The Institute of Statistical Mathematics 1967

Authors and Affiliations

  • Takesi Hayakawa
    • 1
  1. 1.The Institute of Statistical MathematicsTokyoJapan

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