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

This paper studies the capabilities of one dimensional, neighborhood of radius one cellular automata to construct speed one signals. We de/ne the notions of constructibility, consistent constructibility and preserving complexity consistent constructibility. Our main results are the following. • There exists a one dimensional neighborhood of radius one cellular automaton with four states which p...

In this paper we show new formulas for the spectral radius and the spectral subradius of a set of matrices. The advantage of our results is that we express the spectral radius of any set of matrices by the spectral radius of a set of symmetric positive definite matrices. In particular, in one of our formulas the spectral radius is expressed by singular eigenvalues of matrices, whereas in the ex...