kronecker {base}R Documentation

Kronecker products on arrays


Computes the generalised kronecker product of two arrays, X and Y. kronecker(X, Y) returns an array A with dimensions dim(X) * dim(Y).


kronecker(X, Y, FUN = "*", make.dimnames = FALSE, ...)
X %x% Y


X A vector or array.
Y A vector or array.
FUN a function; it may be a quoted string.
make.dimnames Provide dimnames that are the product of the dimnames of X and Y.
... optional arguments to be passed to FUN.


If X and Y do not have the same number of dimensions, the smaller array is padded with dimensions of size one. The returned array comprises submatrices constructed by taking X one term at a time and expanding that term as FUN(x, Y, ...).

%x% is an alias for kronecker (where FUN is hardwired to "*").


Jonathan Rougier,


Shayle R. Searle (1982) Matrix Algebra Useful for Statistics. John Wiley and Sons.

See Also

outer, on which kronecker is built and %*% for usual matrix multiplication.


# simple scalar multiplication
( M <- matrix(1:6, ncol=2) )
kronecker(4, M)
# Block diagonal matrix:
kronecker(diag(1, 3), M)

# ask for dimnames

fred <- matrix(1:12, 3, 4, dimnames=list(LETTERS[1:3], LETTERS[4:7]))
bill <- c("happy" = 100, "sad" = 1000)
kronecker(fred, bill, make.dimnames = TRUE)

bill <- outer(bill, c("cat"=3, "dog"=4))
kronecker(fred, bill, make.dimnames = TRUE)

[Package base version 2.5.0 Index]