Some properties of the Lozinskii logarithmic norm

Аннотация

We study properties of the logarithmic matrix norm. We obtain new estimates for matrix norms as well as for the spectral radius and the spectral abscissa. We give a new proof of the Fiedler theorem and a block test for the Hurwitz property of a matrix based on the theory of nonnegative and off-diagonal-nonnegative matrices.