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As is known to all, the Khatri-Rao product is defined as $\mathbf{C}=\mathbf{A}\odot \mathbf{B}=\left[\begin{matrix}\mathbf{a}_1\otimes\mathbf{b}_1&\mathbf{a}_2\otimes\mathbf{b}_2&\cdots \mathbf{a}_K\otimes\mathbf{b}_K\end{matrix}\right]$,where both $\mathbf{a}_i\in \mathbb{C}^{I\times1}$ $\mathbf{b}_i\in \mathbb{C}^{J\times1}$ and $\mathbf{C} \in \mathbb{C}^{IJ\times K}$. I don't know how to determine the rank of the matrix $\mathbf{C}$,based on the ranks of $\mathbf{A}$ and $\mathbf{B}$.

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  • $\begingroup$ Any references could be found on it? $\endgroup$ – DuWeimin Nov 12 '18 at 3:22

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