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BUILT-IN MATHEMATICA SYMBOL
PillaiTrace
PillaiTrace[m1, m2]
gives Pillai's trace for the matrices 
and 
.
Details
- PillaiTrace[m1, m2] gives Pillai's trace between
and 
. - Pillai's trace is a measure of linear dependence based on partitions of the pooled covariance matrix.
- Pillai's trace is computed as
![Tr[TemplateBox[{{(, {Sigma, _, {(, 11, )}}, )}}, Inverse].Sigma_(12).TemplateBox[{{(, {Sigma, _, {(, 22, )}}, )}}, Inverse].Sigma_(21)]](Files/PillaiTrace.en/6.png "Tr[TemplateBox[{{(, {Sigma, _, {(, 11, )}}, )}}, Inverse].Sigma_(12).TemplateBox[{{(, {Sigma, _, {(, 22, )}}, )}}, Inverse].Sigma_(21)]")
where 
is the covariance matrix of the pooled sample, which can be partitioned into 
where 
and 
correspond to the covariance matrices of the individual datasets. - The arguments
and 
can be any real-valued matrices or vectors of equal length.
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