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'''A'''·'''B''' = '''B'''·'''A''' = '''I'''
== Example 4. ==
A block circulant Jacket matrix (BCJM) is defined by [3, 5]
:<math>
\mathbf{C}_{N}= \left[ \begin{array}{rr} \mathbf{C}_{0} & \mathbf{C}_{1} \\ \mathbf{C}_{1} & \mathbf{C}_{0} \\ \end{array} \right]</math>
be 2x2 block matrix of order N=2p. If <math>[\mathbf{C}_{0}]_p</math> and <math>[\mathbf{C}_{1}]_p </math> are pxp Jacket matrices, then <math>[\mathbf{C}]_N </math> is the Jacket matrix if and only if
:<math>\ \mathbf{C}_{0}\mathbf{C}_{1}^{RT}+\mathbf{C}_{1}^{RT}\mathbf{C}_{0}=0. </math>
where RT is reciprocal transpose.
== Example 5. ==
If p=2, a block circulant Jacket matrix (BCJM) <math>\mathbf{C}_{N} </math>is given by
:<math>
\mathbf{C}_{4}= \left[ \begin{array}{rr} \mathbf{C}_{0} & \mathbf{C}_{1} \\ \mathbf{C}_{1} & \mathbf{C}_{0} \\ \end{array} \right]=\left[
\begin{array}{rrrr} 1 & 1 & a & -a \\[6pt] 1 & -1 & -1/a & -1/a \\[6pt]
a & -a & 1 & 1 \\[6pt] -1/a & -1/a & 1 & -1\\[6pt] \end{array}
\right]_{a=1}=\left[
\begin{array}{rrrr} 1 & 1 & 0 & 0 \\[6pt] 1 & -1 & 0 & 0 \\[6pt]
0 & 0 & 1 & 1 \\[6pt] 0 & 0 & 1 & -1\\[6pt] \end{array}
\right]+\left[
\begin{array}{rrrr} 0 & 0 & 1 & -1 \\[6pt] 0 & 0 & -1 & -1 \\[6pt]
1 & -1 & 0 & 0 \\[6pt] -1 & -1 & 0 & 0\\[6pt] \end{array}
\right]=\left[
\begin{array}{rrrr} 1 & 1 & 1 & -1 \\[6pt] 1 & -1 & -1 & -1 \\[6pt]
1 & -1 & 1 & 1 \\[6pt] -1 & -1 & 1 & -1\\[6pt] \end{array}
\right].</math>
where <math> \mathbf{C}_{0} </math> and <math> \mathbf{C}_{1} </math> are the Hadamard matrix.
== References ==
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