Solving the two-dimensional CIS problem by a rational algorithm
type: Item
instance of: scholarly article
title: Solving the two-dimensional CIS problem by a rational algorithm
zbMATH Open document ID: 0964.65040
DOI: 10.1016/S0024-3795(00)00098-7
author: Yury A. Al'pin
author: Alan George
author: Kh. D. Ikramov
published in: Linear Algebra and its Applications
publication date: 2001-06-26T00:00:00Z
review text: The common invariant subspace (CIS) problem is discussed. Let \(1\leq p< n\) be a fixed integer, and \(A\) and \(B\) are complex matrices. Can one verify whether \(A\) and \(B\) have a common invariant subspace of dimension \(p\) in a finite number of steps? An algorithm is given which solves the problem for \(p=2\). No restrictions are imposed on \(A\) and \(B\). Moreover, when \(A\) and \(B\) generate a semisimple algebra, the algorithm is able to solve the CIS problem for any \(p, 1<p<n\).
reviewed by: Plamen Yalamov
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 1485560
zbMATH Keywords: common invariant subspace
zbMATH Keywords: rational algorithm
zbMATH Keywords: 2-generated matrix algebra
zbMATH Keywords: radical
zbMATH Keywords: socle
zbMATH Keywords: Shemesh's theorem
MaRDI profile type: Publication
cites work: On condensed forms for partially commuting matrices
cites work: A non-commutative spectral theorem
cites work: Common invariant subspaces of two matrices
cites work: Addendum: Is The Polar Decomposition Finitely Computable?
cites work: Q3961610
cites work: Common eigenvectors of two matrices
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description: scientific article; zbMATH DE number 1485560