# kronecker

##### 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.

##### See Also

`outer`

, on which `kronecker`

is built
and `%*%`

for usual matrix multiplication.

##### Examples

`library(base)`

```
# NOT RUN {
# 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 3.4.3, License: Part of R 3.4.3*