Extremal norms of graphs and matrices

Abstract

In recent years, the trace norm of graphs has been extensively studied under the name graph energy. In this paper, this research is extended to more general matrix norms, for example, the Schatten p-norms and the Ky Fan k-norms. Whenever possible, the results are given both for graphs and general matrices. In various contexts, a puzzling fact was observed: the Schatten p-norms are widely different for 1 ≤ p < 2 and for p ≥ 2. © 2012 Springer Science+Business Media, Inc.

Publication Title

Journal of Mathematical Sciences

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