Similarity invariants for pairs of upper triangular Toeplitz matrices. (English) Zbl 0715.15005
The type of matrix A is \(\alpha\), if A can be written as \(A=a_{\alpha}J^{\alpha}+a_{\alpha +1}J^{\alpha +1}+...,\) where \(a_{\alpha}\neq 0\), J is an upper triangular nilpotent \(m\times m\) Jordan block. The following problem is investigated: Let A and Z be matrices of type \(\alpha\) and \(\omega\), respectively. Under what conditions (on \(\alpha\) and \(\omega\)) does there exist an invertible matrix U such that \(U^{-1}AU=J^{\alpha},\quad U^{- 1}ZU=J^{\omega}\).
Reviewer: L.A.Sakhnovich
MSC:
| 15A21 | Canonical forms, reductions, classification |
| 15B57 | Hermitian, skew-Hermitian, and related matrices |
Keywords:
simultaneous reduction; upper triangular Toeplitz matrices; simple matrices; upper triangular nilpotent Jordan block; complementary triangularization of pairs of matricesReferences:
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