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- W4211193273 abstract "This article presents a computable criterion for the existence of a common invariant subspace of $ntimes n$ complex matrices $A_{1}, dots ,A_{s}$ of a fixed dimension $1leq dleq n$. The approach taken in the paper is model-theoretic. Namely, the criterion is based on a constructive proof of the renowned Tarski's theorem on quantifier elimination in the theory $ACF$ of algebraically closed fields. This means that for an arbitrary formula $varphi$ of the language of fields, a quantifier-free formula $varphi'$ such that $varphilravarphi'$ in $ACF$ is given explicitly. The construction of $varphi'$ is elementary and based on the effective Nullstellensatz. The existence of a common invariant subspace of $A_{1},dots,A_{s}$ of dimension $d$ can be expressed in the first-order language of fields, and hence, the constructive version of Tarski's theorem yields the criterion. In addition, some applications of this criterion in quantum information theory are discussed." @default.
- W4211193273 created "2022-02-13" @default.
- W4211193273 creator A5086652323 @default.
- W4211193273 date "2017-02-06" @default.
- W4211193273 modified "2023-10-16" @default.
- W4211193273 title "The common invariant subspace problem and Tarskiâs theorem" @default.
- W4211193273 doi "https://doi.org/10.13001/ela.2017.1783" @default.
- W4211193273 hasPublicationYear "2017" @default.
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