Eigenvalue Decomposition of Paley-Type Hadamard Matrices 


Vol. 43,  No. 6, pp. 902-910, Jun.  2018
10.7840/kics.2018.43.6.902


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  Abstract

In this paper, we determine explicitly the eigenvalue decomposition of Paley-type Hadamard matrices of order pk+1 or 2(pk+1), where p is an odd prime and k is a positive integer. For this, we also determine those of Paley matrices of order pk+1 using those of Jacobsthal matrices of order pk. Some of these results directly applies to any cyclic-type Hadamard matrices. Those results are the first complete description of eigenvalue decompositions of Paley-type or cycic-type Hadamard matrices. All the eigenvector matrices we determined here turned out to be unitary matrices.

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  Cite this article

[IEEE Style]

M. K. Song and H. Song, "Eigenvalue Decomposition of Paley-Type Hadamard Matrices," The Journal of Korean Institute of Communications and Information Sciences, vol. 43, no. 6, pp. 902-910, 2018. DOI: 10.7840/kics.2018.43.6.902.

[ACM Style]

Min Kyu Song and Hong-Yeop Song. 2018. Eigenvalue Decomposition of Paley-Type Hadamard Matrices. The Journal of Korean Institute of Communications and Information Sciences, 43, 6, (2018), 902-910. DOI: 10.7840/kics.2018.43.6.902.

[KICS Style]

Min Kyu Song and Hong-Yeop Song, "Eigenvalue Decomposition of Paley-Type Hadamard Matrices," The Journal of Korean Institute of Communications and Information Sciences, vol. 43, no. 6, pp. 902-910, 6. 2018. (https://doi.org/10.7840/kics.2018.43.6.902)

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pISSN : 1226 - 4717
eISSN : 2287 - 3880