[R] kronecker sum

(Ted Harding)
Sun, 05 Jun 2011 14:37:36 -0000

On 05-Jun-11 13:36:18, Lara Poplarski wrote:
> Dear All,
> Could someone please suggest how to find the Kronecker sum
> of two 2x2 matrices,
> i.e. given two matrices:
>
> -A  A
> a  -a
>
> and
>
> -B   B
> b  -b
>
> I need:
>
>  -A-B    A       B      0
>  a     -a-B     0      B
>  b        0     -A-b  A
>  0        b       a    -a-b
>
> Many thanks,
> Lara

For example, let A=10, a=2, B=5, b=3 so that your

  -A-B     A     B     0
     a  -a-B     0     B
     b     0  -A-b     A
     0     b     a  -a-b

is

  -15  10    5    0
    2  -7    0    5
    3   0  -13   10
    0   3    2   -5

Then, in R,

  M <- matrix(c(-10,10,2,-2),byrow=TRUE,ncol=2)
  N <- matrix(c(-5,5,3,-3),byrow=TRUE,ncol=2)
  I <- diag(1,2,2)

  kronecker(I,M) + kronecker(N,I)
  #      [,1] [,2] [,3] [,4]
  # [1,]  -15   10    5    0
  # [2,]    2   -7    0    5
  # [3,]    3    0  -13   10
  # [4,]    0    3    2   -5

See '?kronecker'.

Hoping this helps.
Ted.

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Date: 05-Jun-11                                       Time: 15:37:32
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