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Canonical forms, higher rank numerical range, convexity, totally isotropic subspace, matrix equations

open access: yes, 2007
Results on matrix canonical forms are used to give a complete description of the higher rank numerical range of matrices arising from the study of quantum error correction. It is shown that the set can be obtained as the intersection of closed half planes (of complex numbers). As a result, it is always a convex set in $\mathcal C$. Moreover, the higher
Li, Chi-Kwong, Sze, Nung-Sing
openaire   +2 more sources

Canonical forms for pairs of matrices associated with Lagrangian and Dirac subspaces

open access: yes
We derive the canonical forms for a pair of $n\times n$ complex matrices $(E,Q)$ under transformations $(E,Q) \rightarrow (UEV,U^{-T}QV)$, and $(E,Q) \rightarrow (UEV,U^{-*}QV)$, where $U$ and $V$ are nonsingular complex matrices. We, in particular, consider the special cases of $E^TQ$ and $E^*Q$ being (skew-)symmetric and (skew-)Hermitian ...
Das, Sweta   +2 more
openaire   +2 more sources

Lagrangian Relations and Quantum L ∞ Algebras. [PDF]

open access: yesCommun Math Phys
Jurčo B, Pulmann J, Zika M.
europepmc   +1 more source

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