Abstract
Singular values are introduced and studied for pencils A — λG of selfadjoint matrices which for some values of λ are positive definite. These singular values describe the widths of certain unbounded sets.
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References
Asher Ben-Artzi and Israel Gohberg, Singular Numbers of Contractions in Spaces with an Indefinite Metric, to appear.
Israel Gohberg and Mark Krein, Introduction to the Theory of Linear Non-selfadjoint Operators, Translations of Mathematicsal Monographs, Vol. 18, American Mathematical Society, Providence, Rhode Island, 1969.
Peter Lancaster and Miron Tismenetsky, The Theory of Matrices, Second Edition with Applications (Computer Science and Applied Mathematics), Academic Press, Inc., Orlando, 1985.
Allan Pinkus, n-Widths in Approximation Theory (Ergebnisse der Mathematik und ihrer Grenzgebiete; 3. Folge, Band 7), Springer-Verlag, Berlin Heidelberg, 1985.
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Dedicated to Professor Heinz Langer on the occasion of his 60-th birthday
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© 1998 Springer Basel AG
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Ellis, R.L., Gohberg, I., Lay, D.C. (1998). Singular values of positive pencils and applications. In: Dijksma, A., Gohberg, I., Kaashoek, M.A., Mennicken, R. (eds) Contributions to Operator Theory in Spaces with an Indefinite Metric. Operator Theory Advances and Applications, vol 106. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8812-7_6
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DOI: https://doi.org/10.1007/978-3-0348-8812-7_6
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9782-2
Online ISBN: 978-3-0348-8812-7
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