On the characterization of the extremal points of the unit sphere of matrices (Q1107600)

The author investigates the unit sphere of the \(m\times n\) matrices with respect to a unitarily invariant norm. It is known that corresponding to the norm there is a symmetric gauge-function oft \(t=\min (m,n)\) variables such that the norm of the matrix equals the value of the gauge-function at the \(t\)-vector of singular values of the matrix. He shows that a matrix is an extremal point of the unit sphere if and only if the vector of singular values is extremal in the unit sphere in \(t\)-dimensional space equipped with the norm which equals the symmetric gauge-function. Properties of dual matrices are also investigated.