non linear correlation for three vectors

I have a matrix that includes three columns of values. Thus, how can I measure the nonlinear correlation of these vectors?

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dpb
dpb 2020 年 6 月 26 日
Which measure would you propose to compute?
I know of no widely accepted statistic (doesn't say there isn't one; but I'm unaware of it and a QDAGS didn't locate anything other than a research paper or two).

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dpb
2020 年 6 月 26 日

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