The faces of the unit balls of \(c\)-norms and \(c\)-spectral norms. (English) Zbl 0923.15014
Summary: We give a complete description of the faces of the closed unit ball of an arbitrary \(c\)-norm on \(\mathbb{R}^n\), and we determine the barycenter, the volume, and the symmetries of each face. As a consequence of a previous result we characterize the faces of the closed unit ball of the corresponding \(c\)-spectral norm on the space of \(n\times m\) real (or complex) matrices.
MSC:
| 15A60 | Norms of matrices, numerical range, applications of functional analysis to matrix theory |
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