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==Bivariate case==
The optical transformation <math>\theta^*(Y), \varphi^*(X)</math> for <math>p=1</math> satisfies
: <math> \rho^*(X, Y) = \rho^*(\theta^*, \varphi^*) = \max_{\theta, \varphi} \rho
where <math>\rho</math> is [[Pearson correlation coefficient]]. <math> \rho^*(X, Y)</math> is known as the maximal correlation between <math>X</math> and <math>Y</math>. It can be used as a general measure of dependence.
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