I have a large vector with complex numbers.
- How do I check whether it a conjugate symmetry vector?
- If not, is there any way to transform it?
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$\begingroup$ Do you mean a large matrix? $\endgroup$– fredJun 7 '16 at 14:35
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$\begingroup$ @fred No. I have edited my answer to include the central definition which was also new to me. $\endgroup$– Carl ChristianJun 7 '16 at 16:18
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You reverse the order of the components of a vector with the "flip" command. Complex conjugation is done with the "conj" command. So, you will want to check if conj(flip(x)) equals x or not.
EDIT: The term conjugate symmetric vector was new to me. It appears to be a term used exclusively by some members of the signal processing community. A vector $x \in \mathbb{C}^n$ is conjugate symmetric if and only if $x = J_n\, \bar{x}$, where $J_n$ denotes the $n$ by $n$ anti-diagonal exchange matrix and $\bar{x}$ denotes complex conjugation. The action of $J_n$ on a vector $x \in \mathbb{C}^n$ consists of reversing the order of the elements of $x$.
