Dear All

I am kind of stuck up with a code a part of which seems to be causing a
problem, or at least I think so. May be the community can help me. It’s
simple but I suppose I am missing something.

I generate a data matrix X, say of order n*p, where n represents
independent row-vectors and p correlated col vectors. Let the row
representation be X = (X'_1, . . ., X'_n)'. I generate the differences of
these vectors as D_{ab} = X_a – X_b, with different indices a and b, and
similarly D_{cd} = X_c – X_d, and make a quadratic form D'_{ab}D_{cd} =
A_{abcd}, say. Please note that, here a is unequal b, c is unequal d, a is
unequal c, b is unequal d.

By slightly shuffling the same set of vectors, I generate two other similar
quadratic forms, say A_{acbd} and A_{adcb}, where the indices are again as
unequal as stated above.

In the R-code (a part of ) below, I compute these three forms using pata,
patb, patc, respectively, using kronecker products. But from the final
result of this code I get the feeling there is a difference between what I
want the code to do and what it actually does.

 en <- matrix(1, n, 1)

 jn <- matrix(1, n, n)

 dev  <- jn - diag(n)

 pata <- dev%x%dev

 patb <- jn%x%jn - diag(n)%x%diag(n)

 patc <- jn%x%diag(n) - diag(n)%x%jn



Any help will be sincerely appreciated!



Best regards

RA

	[[alternative HTML version deleted]]

