Abstract
Van Dooren [Linear Algebra Appl. 27 (1979) 103] constructed an algorithm for the computation of all irregular summands in Kronecker’s canonical form of a matrix pencil. The algorithm is numerically stable since it uses only unitary transformations. We construct a unitary algorithm for computation of the canonical form of the matrices of a chain of linear mappings V 1—V 2—⋯—V t andextend Van Dooren’s algorithm to the matrices of a cycle of linear mappings whereall V i are complex vector spaces and each line denotes → or ←.
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