`kronecker.prod`

Kronecker product on matrices

Description

Computes the kronecker product of two matrices, x and y .

Usage

kronecker.prod(x, y = x)

Arguments

Argument	Description
`x`	a numeric matrix or vector.
`y`	a numeric matrix or vector.

Details

Let \(\mathbf{X}\) be an \(m\times n\) and \(\mathbf{Y}\) a \(p\times q\) matrix. The \(mp\times nq\) matrix defined by

\[\left[{\begin{array}{*{20}{c}}x_{11}\mathbf{Y} & \dots & x_{1n}\mathbf{Y} \\\vdots & & \vdots \\x_{m1}\mathbf{Y} & \dots & x_{mn}\mathbf{Y}\end{array}}\right],\]

is called the Kronecker product of \(\mathbf{X}\) and \(\mathbf{Y}\) .

Value

An array with dimensions dim(x) * dim(y) .

References

Magnus, J.R., Neudecker, H. (2007). Matrix Differential Calculus with Applications in Statistics and Econometrics , 3rd Edition. Wiley, New York.

Examples

# block diagonal matrix:
a <- diag(1:3)
b <- matrix(1:4, ncol = 2)
kronecker.prod(a, b)

# examples with vectors
ones <- rep(1, 4)
y <- 1:3
kronecker.prod(ones, y) # 12-dimensional vector
kronecker.prod(ones, t(y)) # 3 x 3 matrix

kronecker.prod