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On Eigenvalues of Row-Inverted Sylvester Hadamard Matrices

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Abstract.

In this paper, the eigenvalues of row-inverted 2n × 2n Sylvester Hadamard matrices are derived. Especially when the sign of a single row or two rows of a 2n × 2n Sylvester Hadamard matrix are inverted, its eigenvalues are completely evaluated. As an example, we completely list all the eigenvalues of 256 different row-inverted Sylvester Hadamard matrices of size 8.

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Authors and Affiliations

  1. jFinger Co., Ltd. and the Institute of New Media and Communications, Seoul National University, Seoul, 151-744, Korea

    Seung-Rae Lee

  2. The Department of Electrical Engineering and Computer Science and INMC, Seoul National University, Seoul, 151-744, Korea

    Jong-Seon No

  3. Homecast Co. Ltd., Seoul, 138-803, Korea

    Eun-Ho Shin

  4. The School of Electronics and Electrical Engineering, Hongik University, Seoul, 121-791, Korea

    Habong Chung

Authors
  1. Seung-Rae Lee
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  2. Jong-Seon No
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  3. Eun-Ho Shin
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  4. Habong Chung
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Corresponding author

Correspondence to Seung-Rae Lee.

Additional information

Received: July 17, 2008; Revised: July 24, 2008.

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Lee, SR., No, JS., Shin, EH. et al. On Eigenvalues of Row-Inverted Sylvester Hadamard Matrices. Results. Math. 54, 117–126 (2009). https://doi.org/10.1007/s00025-008-0322-4

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  • DOI: https://doi.org/10.1007/s00025-008-0322-4

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