The problem of finding mr(F,G) and describing Gk(F ) has recently attracted considerable attention, particularly for the case in which F = R (see [29, 17, 26, 25, 27, 13, 33, 5, 9, 22, 2, 11, 6, 7, 10, 18, 4]). The minimum rank problem over R is a sub-problem of a much more general problem, the inverse eigenvalue problem for symmetric matrices: given a family of real numbers, find every symmetr...

In this paper we construct the symmetric quasi anti-bidiagonal matrix that its eigenvalues are given, and show that the problem is also equivalent to the inverse eigenvalue problem for a certain symmetric tridiagonal matrix which has the same eigenvalues. Not only elements of the tridiagonal matrix come from quasi anti-bidiagonal matrix, but also the places of elements exchange based on some co...

In the past few years transmission eigenvalues have become an important area of research in inverse scattering theory with active research being undertaken in many parts of the world. Transmission eigenvalues appear in the study of scattering by inhomogeneous media and are closely related to non-scattering waves. Such eigenvalues provide information about material properties of the scattering m...

In linear stability analysis of a large-scale dynamical system, we need to compute the rightmost eigenvalue(s) for a series of large generalized eigenvalue problems. Existing iterative eigenvalue solvers are not robust when no estimate of the rightmost eigenvalue(s) is available. In this study, we show that such an estimate can be obtained from Lyapunov inverse iteration applied to a special ei...

In this paper, we investigate a direct and an inverse eigenvalue problem to recover doubly periodic pseudo-Jacobi matrices from three spectra ?, ?1, ?2 two positive numbers ??, ??. Necessary sufficient conditions for the existence of solution are given numerical algorithms, using modified unsymmetric Lanczos scheme, reconstruct matrix prescribed data proposed. Some illustrative examples present...