We present a short and simple proof of the well-known Cauchy interlace theorem. We use the theorem to improve some lower bound estimates for the spectral radius of a real symmetric matrix.

Determination of the regularity radius r∗ of interval matrices is known to be a NP-hard problem. In this paper, a method for determining r∗ is suggested whose numerical complexity is not a priori exponential. The method is based on an equivalent transformation of the original problem to the problem of determining the real maximum magnitude eigenvalue μ∗ of an associated interval generalized eig...

Recently, Uhlig [Numer. Algorithms, 52(3):335-353, 2009] proposed open questions about the ratios between the spectral norm, the numerical radius and the spectral radius of a square matrix. In this note, we provide some observations to answer these questions. Keywords—Spectral norm, Numerical radius, Spectral radius, Ratios