PCA on complex-valued data

Question

What's the correct way to undertake PCA on complex-valued data?

I see that this solution exists.

Are there any python packages that have implemented a complex-PCA?

So far I have just broken my data into real and imaginary parts and performed PCA as if they were real. For example:

| sw  | fw | mw |
|4+4i |3+2i|1-1i|

would become:

| swreal | swimag | fwreal | fwimag | mwreal | mwimag |
|   4    |    4   |    3   |    2   |   1    |   -1   |

My PCA ends up looking like this:

I want to pursue a complex PCA, but I'm not even sure how I would end up representing it? If it were a 2D plot, the only way is similar to above(?), in which case, would it look any different?