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  Volume 7, Issue 5, Article 195
On the Bounds for the Spectral and $\ell _p$ Norms of the Khatri-Rao Product of Cauchy-Hankel Matrices

    Authors: Hacı Civciv, Ramazan Türkmen,  
    Keywords: Cauchy-Hankel matrices, Kronecker product, Khatri-Rao product, Tracy-Singh product, Norm.  
    Date Received: 21/07/05  
    Date Accepted: 10/05/06  
    Subject Codes:

15A45, 15A60, 15A69.

    Editors: Fuzhen Zhang,  

In this paper we first establish a lower bound and an upper bound for the $ ell _{p}$ norms of the Khatri-Rao product of Cauchy-Hankel matrices of the form $ H_{n}$= $ left[ 1/left( g+(i+j)hright) right] _{i,j=1}^{n}$ for $ g=1/2$ and $ h=1$ partitioned as

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}
where $ H_{n}^{(ij)}$ is the $ ij$th submatrix of order $ m_{i}times n_{j}$ with $ H_{n}^{(11)}=H_{n-1}$. 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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