[R] Multiple operations on list

[Stephane DRAY]

Hello,

suppose I have a list with matrices:

a=list(x1=matrix(rnorm(10),5,2),x2=matrix(rnorm(10),5,2),x3=matrix(rnorm(10),5,2))

I want to compute for all combination of xi and xj (x1,x2 x1,x3 and x2,x3) 
a value.
This value is given for the pair x1,x2 by trace(x1%*%t(x1)%*%x2%*%t(x2)) / 
trace(x1%*%t(x1))*trace(x2%*%t(x2))

I know that product matrices t(xi)%*%xi can be obtained by:

aa=lapply(a,crossprod)

but I do not know how to "mix" the values in aa to obtain the desired values.

Is there a way to do it without for loop ?

Thanks in advances,

sincerely

Stéphane DRAY
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Département des Sciences Biologiques
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E-mail : stephane.dray at umontreal.ca
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