# kronecker: Kronecker Products on Arrays

 kronecker R Documentation

## Kronecker Products on Arrays

### Description

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

### 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)`.

Jonathan Rougier

### 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.

### Examples

```# 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)
```