Abstract
The problem considered is the following. Given two upper triangular Toeplitz matrices A and Z, when does there exist an invertible matrix S such that S −1 AS is upper triangular and S −1 ZS is lower triangular? The motivation for considering simultaneous reduction to complementary triangular forms of pairs of matrices comes from systems theory. For upper triangular Toeplitz matrices, a complete answer is given. The argument involves a detailed analysis of a certain directed graph associated with A and Z. Along the way information is obtained about the structure of the similarity S. The results actually hold for a class of matrices strictly larger than that consisting of the upper triangular Toeplitz matrices.
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Dedicated to Israel Gohberg on the occasion of his sixtieth birthday, with admiration
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© 1989 Birkhäuser Verlag Basel
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Bart, H., Thijsse, G.P.A. (1989). Complementary Triangular Forms of Upper Triangular Toeplitz Matrices. In: Dym, H., Goldberg, S., Kaashoek, M.A., Lancaster, P. (eds) The Gohberg Anniversary Collection. Operator Theory: Advances and Applications, vol 40. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9276-6_5
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DOI: https://doi.org/10.1007/978-3-0348-9276-6_5
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9974-1
Online ISBN: 978-3-0348-9276-6
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