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Volume 7, Issue 5, Article 195 |
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On the Bounds for the Spectral and $\ell _p$ Norms of the Khatri-Rao Product of Cauchy-Hankel Matrices
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Authors: |
Hacı Civciv, Ramazan Türkmen, |
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Keywords:
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Cauchy-Hankel matrices, Kronecker product, Khatri-Rao product, Tracy-Singh product, Norm. |
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Date Received:
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21/07/05 |
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Date Accepted:
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10/05/06 |
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Subject Codes: |
15A45, 15A60, 15A69.
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Editors: |
Fuzhen Zhang, |
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Abstract: |
In this paper we first establish a lower bound and an upper bound for the  norms of the Khatri-Rao product of Cauchy-Hankel matrices of the form  = ![$ left[ 1/left( g+(i+j)hright) right] _{i,j=1}^{n}$](images/223_05_JIPAM/img3.gif) for  and  partitioned as where  is the  th submatrix of order  with  . We then present a lower bound and an upper bound for the spectral norm of Khatri-Rao product of these matrices.
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![begin{displaymath} H_{n}=left( begin{array}{cc} H_{n}^{(11)} & H_{n}^{(12)} [5pt] H_{n}^{(21)} & H_{n}^{(22)} end{array}right) end{displaymath}](images/223_05_JIPAM/img6.gif)
