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Recent Advances in Matrix and Operator Theory pp 35–46Cite as

Ranks of Hadamard Matrices and Equivalence of Sylvester—Hadamard and Pseudo-Noise Matrices

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

Abstract

In this paper we obtain several results on the rank properties of Hadamard matrices (including Sylvester-Hadamard matrices) as well as generalized Hadamard matrices. These results are used to show that the classes of (generalized) Sylvester-Hadamard matrices and of (generalized) pseudo-noise matrices are equivalent, i.e., they can be obtained from each other by means of row/column permutations.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Connecticut, Storrs, CT, 06269-3009, USA

    Tom Bella & Vadim Olshevsky

  2. 735 Crawford Avenue, Brooklyn, NY, 11223, USA

    Lev Sakhnovich

Authors
  1. Tom Bella
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  2. Vadim Olshevsky
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  3. Lev Sakhnovich
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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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Bella, T., Olshevsky, V., Sakhnovich, L. (2007). Ranks of Hadamard Matrices and Equivalence of Sylvester—Hadamard and Pseudo-Noise Matrices. 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_3

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