MAX-MIN PROPERTIES OF MATRIX FACTOR NORMS

Given a set of real matrices C0, C1,..., C(k), conditions are considered under which the equality [GRAPHICS] holds. It is shown that if the matrices C(i), i = 0, 1,..., k are normal and commute with one another, then the equality holds. In particular, this implies that if C(i) = A(i) or C(i) = Ak-i, where A is a normal matrix, then the equality holds. An example is given to show that the equality may fail for noncommuting matrices, when k > 1. It is shown that the equality holds for arbitrary matrices if k = 1.