More Lyapunov-Loewy type results (Q2850049)
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scientific article; zbMATH DE number 6212304
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | More Lyapunov-Loewy type results |
scientific article; zbMATH DE number 6212304 |
Statements
26 September 2013
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Lyapunov transformation
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inverse
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Hermitian preserving
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inertia
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simultaneous triangulability
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ranges
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More Lyapunov-Loewy type results (English)
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Let \(M_n\) be the space of \(n\times n\) complex matrices and \(\mathcal {H}_n\) be the Hermitian subcone of \(M_n\). For a fixed matrix \(A\in M_n\), the Lyapunov transformation \(T_A: \mathcal {H}_n\to \mathcal{H}_n\) is defined by \(T_A(H)=AH+HA^*\).NEWLINENEWLINEThe study of the ranges of Lyapunov transformations was initiated by \textit{D. Carlson} and \textit{R. Loewy} [Linear Algebra Appl. 8, 237--248 (1974; Zbl 0284.15013)]. In the paper under review, the authors obtain several new results on the ranges of Lyapunov transformations by extending some well-known results.
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0.7538696527481079
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0.740494966506958
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0.7284637689590454
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