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If <math>[\mathbf {A}_0]_p</math> and <math>[\mathbf {A}_1]_p</math> are pxp Jacket matrix, then <math>[A]_N</math> is a block circulant matrix if and only if <math>\mathbf {A}_0 \mathbf {A}_1^{rt}+\mathbf {A}_1^{rt}\mathbf {A}_0</math>, where rt denotes the reciprocal transpose.
== Example 5. ==
Let <math>\mathbf {A}_0== \left[ \begin{array}{rrrr} 1 & 1 \\ 1 & -1\\ \end{array} \right],</math> and <math>\mathbf {A}_1== \left[ \begin{array}{rrrr} a & -a \\ 1/a & -1/a\\ \end{array} \right],</math>, then the matrix <math>[\mathbf {A}]_N</math> is given by
:<math>
[\mathbf {A}]_4= \left[ \begin{array}{rrrr} 1 & 1 & a & -a \\ 1 & -1 & 1/a & -1/a \\ 1 & 1 & a & -a \\ 1 & -1 & 1/a & -1/a \\ \end{array} \right],</math>:<math>
when N=2p and p=2.
== References ==
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[3] Moon Ho Lee, ''Jacket Matrices: Constructions and Its Applications for Fast Cooperative Wireless Signal Processing'', LAP LAMBERT Publishing, Germany, Nov. 2012.
[4] Moon Ho Lee, et. al., "MIMO Communication Method and System using the Block Circulant Jacket Matrix," US patent, no. US 009356671B1, 3May, 2016.
==External links==
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