# kronecker

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##### Kronecker Products on Arrays

Computes the generalised kronecker product of two arrays, X and Y.

Keywords
array
##### Usage
kronecker(X, Y, FUN = "*", make.dimnames = FALSE, ...)
X %x% Y
##### Arguments
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.
##### Details

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 "*").

##### Value

An array A with dimensions dim(X) * dim(Y).

##### References

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

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

• kronecker
• .kronecker
• %x%
##### Examples
library(base) # 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) 
Documentation reproduced from package base, version 3.3, License: Part of R @VERSION@

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