Generalized Shemesh criterion, common invariant subspaces and irreducible completely positive superoperators

DOI10.1080/03081087.2013.865734zbMath1308.15008arXiv1306.0083OpenAlexW2963414440MaRDI QIDQ2938340

Grzegorz Pastuszak, Andrzej Jamiołkowski

Publication date: 14 January 2015

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.0083

zbMATH Keywords

algorithmnumerical exampleirreducible operatorscommon invariant subspacescomputation complexitycommon eigenvectorscompletely positive superoperatorShemesh criterion

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Invariant subspaces of linear operators (47A15) Complexity and performance of numerical algorithms (65Y20)

Related Items (9)

On invariant subspace in quantum control systems and some concepts of integrable quantum systems ⋮ Algebraic method in the analysis of decoherence-free subspaces in open quantum systems ⋮ On maps which preserve semipositivity and quantifier elimination theory for real numbers ⋮ Ascending chains of ideals in the polynomial ring ⋮ Quantifier elimination theory and maps which preserve semipositivity ⋮ Stability of simultaneously block triangularisable switched systems with partial state reset ⋮ On a Criterion for Simultaneous Block-Diagonalization of Normal Matrices ⋮ Some remarks on the Shifner-Erougin-Salakhova-Chebotarev type differential equations ⋮ Algebraic reduction methods and their applications to matrix continued fractions

Cites Work

• Around the circular law
• Common eigenvectors of two matrices
• Common invariant subspaces of two matrices
• Rational procedures in the problem of common invariant subspaces of two matrices
• Solving the two-dimensional CIS problem by a rational algorithm
• A criterion for the existence of common invariant subspaces of matrices
• The common invariant subspace problem: an approach via Gröbner bases
• EFFECTIVE METHODS IN INVESTIGATION OF IRREDUCIBLE QUANTUM OPERATIONS
• Quantum Computation and Quantum Information
• The Mathematical Language of Quantum Theory
• Irreducible positive linear maps on operator algebras
• Invariant Subspaces of Matrices with Applications

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