The distribution of genetic variance in multivariate phenotypes is characterized by the empirical spectral distribution of the eigenvalues of the genetic covariance matrix. Empirical estimates of genetic eigenvalues from random effects linear models are known to be overdispersed by sampling error, where large eigenvalues are biased upward, and small eigenvalues are biased downward. The overdisp...

Let G be a simple graph with n(≥ 2) vertices, and λi(G) be the ith largest eigenvalue of G. In this paper we obtain the following: If λ3(G) < 0, and there exists some index k, 2 ≤ k ≤ [n2 ],such that λk(G) = -1, then λj(G) = −1, j = k, k + 1, · · · , n− k + 1. In particular, we obtain that (1) λ2(G) = −1 implies λ1(G) = n− 1, λj(G) = −1, j = 2, 3, · · · , n. and therefore G is complete. This is...

Dynamic characteristics of linear structural systems are governed by the natural frequencies and the mode-shapes. In this paper the statistical properties of the eigenvalues of linear dynamic systems are considered. It is assumed that the mass and the stiffness matrices are smooth, continuous and at least twice differentiable functions of a random parameter vector. The random parameter vector i...