Block Kronecker products and block norm matrices in large-scale systems analysis. (English) Zbl 0665.15015
The paper deals with adequate extensions of the Kronecker product and of the matrix norm in the case of block-partitioned matrices. Correspondingly, algebraic properties and respectively related equalities and inequalities are derived. Some results concerning block-diagonal matrices are also developed in order to derive in implified fashion the covariance block norm inequality proved by the first author and D. S. Bernstein [IEEE Trans. Autom. Control AC-32, 1005-1013 (1987; Zbl 0643.93006)].
Reviewer: M.Voicu
MSC:
| 15B57 | Hermitian, skew-Hermitian, and related matrices |
| 15A24 | Matrix equations and identities |
| 15A45 | Miscellaneous inequalities involving matrices |
| 93A15 | Large-scale systems |
| 15A60 | Norms of matrices, numerical range, applications of functional analysis to matrix theory |
