Abstract
Let O be the operation which for any n × n complex matrix replaces all its diagonal entries by zeroes. For various matrix norms, we study max A |||OA|||/|||A|||. Upper and lower bounds are obtained, but they agree only for the c p norms with p = 1, 2, ∞. For these latter norms, the value of the maximum is also obtained with A restricted to the subset A ≥ 0.
This author thanks the University of Toronto and NSERC (Canada) for a visit during which some of this work was done.
This author thanks the Indian Statistical Institute and NSERC (Canada) for a visit during which some of this work was done.
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Dedicated to Israel Gohberg on the occasion of his sixtieth birthday.
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© 1989 Birkhäuser Verlag Basel
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Bhatia, R., Choi, MD., Davis, C. (1989). Comparing a Matrix to its Off-Diagonal Part. In: Dym, H., Goldberg, S., Kaashoek, M.A., Lancaster, P. (eds) The Gohberg Anniversary Collection. Operator Theory: Advances and Applications, vol 40/41. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-9144-8_4
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DOI: https://doi.org/10.1007/978-3-0348-9144-8_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9924-6
Online ISBN: 978-3-0348-9144-8
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