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. Its
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
MR Ahmad
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