Optimally conditioned block matrices Original Research Article

The paper provides a description of optimally conditioned Hermitian positive-definite block matrices, i.e., of matrices image , ngreater-or-equal, slantedmgreater-or-equal, slanted2, image ,i=1,…,m, such that image Here, image is the group of nonsingular block diagonal matrices with diagonal blocks of orders ni, i=1,…,m, and k(A) is the spectral condition number of A. The results obtained generalize those for the particular cases m=n and m=2, see [Proc. Amer. Math. Soc. 6 (1955) 340 and Zap. Nauchn. Sem. POMI, 268 (2000) 72], respectively.