Eigenvalues of sample covariance matrices are often used in biometrics. It has been known for several decades that even though the sample covariance matrix is an unbiased estimate of the real covariance matrix [3], the eigenvalues of the sample covariance matrix are biased estimates of the real eigenvalues [6]. This bias is particularly dominant when the number of samples used for estimation is...

The paper studies the eigenvalue distribution of Schur complements of some special matrices, including nonstrictly diagonally dominant matrices and general H−matrices. Zhang, Xu, and Li [Theorem 4.1, The eigenvalue distribution on Schur complements of H-matrices. Linear Algebra Appl., 422:250–264, 2007] gave a condition for an n×n diagonally dominant matrix A to have |JR+(A)| eigenvalues with p...

Ostrowski type and Brauer type theorems are derived for the left eigenvalues of quaternionic matrix. We see that the above theorems for the left eigenvalues are also true for the case of right eigenvalues, when the diagonals of quaternionic matrix are real. Some distribution theorems are given in terms of ovals of Cassini that are sharper than the Ostrowski type theorems, respectively, for the ...

We consider a PT-symmetric partner to Khare-Mandal’s recently proposed non-Hermitian potential with complex eigenvalues. Our potential, which is quasi-exactly solvable, is shown to possess only real eigenvalues. PACS : 03.65.Bz, 03.65.Ge

Abstract In this article, we express the eigenvalues of real antitridiagonal Hankel matrices as zeros given rational functions. We still derive eigenvectors for these structured at expense prescribed eigenvalues.

In this paper bounds for clusters of eigenvalues of non-selfadjoint matrices are investigated. We describe a method for the computation of rigorous error bounds for multiple or nearly multiple eigenvalues, and for a basis of the corresponding invariant subspaces. The input matrix may be real or complex, dense or sparse. The method is based on a quadratically convergent Newton-like method; it in...