The common invariant subspace problem: an approach via Gröbner bases

DOI10.1016/j.laa.2003.03.001zbMath1067.15002OpenAlexW2022716134MaRDI QIDQ1827474

Chris Peterson, Donu Arapura

Publication date: 6 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.laa.2003.03.001

zbMATH Keywords

AlgorithmGröbner basisGrassmann varietyInvariant subspaceEigenvector

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (8)

Deciding the boundedness and dead-beat stability of constrained switching systems ⋮ Linear switched dynamical systems on graphs ⋮ Generalized Shemesh criterion, common invariant subspaces and irreducible completely positive superoperators ⋮ Ascending chains of ideals in the polynomial ring ⋮ A height gap theorem for coefficients of Mahler functions ⋮ Common eigenvector approach to exact order reduction for Roesser state-space models of multidimensional systems ⋮ An algorithmic approach to simultaneous triangularization ⋮ Simultaneous block diagonalization of matrices of finite order

Cites Work

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• Common eigenvectors of two matrices
• Direct methods for primary decomposition
• 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

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