What is the dual matrix (of a sample covariance matrix)?

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Let $A$ be a matrix. I am most interested in the real, symmetric case, but for full understanding let's let $A$ be complex. What does it mean for $A^D$ to be the dual matrix of $A$?

Can we interpret it in terms of the SVD of $A=U\Sigma U^T$?

Note: This is not merely the transpose. See 6.1 in for an example of this term.

I've included the tags random matrices and probability distributions since that has something to do with the unconventional context in which I found this term used. I do not know to what extent they are relevant.

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1 Answer

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I have heard about dual matrix (of vector) in Computer Graphics course. It was presented in context of cross product and noted as $A^*$ (A-star). So it was conjugate-transpose matrix. Good explanation is here.

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