On the unitarily invariant norms and some related results
Chi-Kwong Li, Nam‐Kiu Tsing · Linear and Multilinear Algebra · 1987
A norm N defined on the linear space of n × n complex matrices (denoted by ) is said to be unitarily invariant if for any A in and n × n unitary matrix U. In this note we study the properties of unitarily invariant norms. Using the metric properties of with respect to this kind of norms, we characterize different classes of matrices such as normal, unitary. Hermitian, positive semi-definite matrices etc. Some approximation problems in are also investigated.