On limit theorem for the eigenvalues of product of two random matrices
The existence of limiting spectral distribution (LSD) of the product of two random matrices is proved. One of the random matrices is a sample covariance matrix and the other is an arbitrary Hermitian matrix. Specially, the density function of LSD of SnWn is established, where Sn is a sample covariance matrix and Wn is Wigner matrix.
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Volume (Year): 98 (2007)
Issue (Month): 1 (January)
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References listed on IDEAS
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- Yin, Y. Q., 1986. "Limiting spectral distribution for a class of random matrices," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 50-68, October.
- Yin, Y. Q. & Bai, Z. D. & Krishnaiah, P. R., 1983. "Limiting behavior of the eigenvalues of a multivariate F matrix," Journal of Multivariate Analysis, Elsevier, vol. 13(4), pages 508-516, December.
- Yin, Y. Q. & Krishnaiah, P. R., 1983. "A limit theorem for the eigenvalues of product of two random matrices," Journal of Multivariate Analysis, Elsevier, vol. 13(4), pages 489-507, December.
- Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
- Silverstein, J. W. & Bai, Z. D., 1995. "On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 175-192, August.
- Bai, Z. D. & Yin, Y. Q. & Krishnaiah, P. R., 1986. "On limiting spectral distribution of product of two random matrices when the underlying distribution is isotropic," Journal of Multivariate Analysis, Elsevier, vol. 19(1), pages 189-200, June.
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