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A Matrix and its Inverse: Revisiting Minimal Rank Completions

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Recent Advances in Matrix and Operator Theory

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 179))

Abstract

We revisit a formula that connects the minimal ranks of triangular parts of a matrix and its inverse and relate the result to structured rank matrices. We also address a generic minimal rank problem that was proposed by David Ingerman and Gilbert Strang.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Drexel University, 3141 Chestnut Street, Philadelphia, PA, 19104, USA

    Hugo J. Woerdeman

Authors
  1. Hugo J. Woerdeman
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA

    Joseph A. Ball

  2. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    Yuli Eidelman

  3. Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, California, 92093-0112, USA

    J. William Helton

  4. Department of Mathematics, University of Connecticut, 196 Auditorium Road, U-9, Storrs, CT, 06269, USA

    Vadim Olshevsky

  5. Department of Mathematics, University of Virginia, P. O. Box 400137, Charlottesville, VA, 22904-4137, USA

    James Rovnyak

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Woerdeman, H.J. (2007). A Matrix and its Inverse: Revisiting Minimal Rank Completions. In: Ball, J.A., Eidelman, Y., Helton, J.W., Olshevsky, V., Rovnyak, J. (eds) Recent Advances in Matrix and Operator Theory. Operator Theory: Advances and Applications, vol 179. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8539-2_19

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