A note on simultaneously diagonalizable matrices. (English) Zbl 0889.15009
The authors consider the problem of maximizing the functional
\[
f(U)= \sum^n_{i=1} \max_j \{(U^T M_jU)_{ii}\}
\]
over all \(n\times n\) orthogonal matrices \(U\) and show that any orthogonal matrix \(Q\) which simultaneously diagonalizes the \(M_j\) maximizes \(f\).
Reviewer: P.Narain (Bombay)
MSC:
15A21 | Canonical forms, reductions, classification |
15A45 | Miscellaneous inequalities involving matrices |