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: As you probably know, conjugate transpose is a generalization of plain old transpose that allows these operations to work on complex numbers instead of just real numbers. If the source data '''X''' consists entirely of real numbers, then the conjugate operation is completely transparent, since the conjugate of a real number is the number itself. But if the source data includes complex numbers, then the conjugate operations is absolutely essential for the matrix operations to yield meaningful results. As far as I can tell, it ''does'' work on complex numbers. As an example where you might have complex numbers as source data, you might want to use PCA on the Fourier components of a real, discrete-time signal, which are in general complex. -- [[User:Metacomet|Metacomet]] 18:59, 1 January 2006 (UTC)
::I have added a motivation paragraph at [[Conjugate_transpose#Motivation]] to try to show why it is so natural for the conjugate transpose to turn up, whenever the matrix you're transposing includes complex numbers. Hope it's helpful. -- [[User:Jheald|Jheald]] 20:14, 12 January 2006 (UTC).
== Computation ==
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