kronecker sum

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

Why not do it in the obvious way?

A <- matrix1[1,2]
a <- matrix1[2,1]
B <- matrix2[1,2]
b <- matrix2[2,1]
matrix(c(-A-B,a,b,0,  A,-a-B,0,b, B,0,-A-b,a, 0,B,A,-a-b), 4,4)

Duncan Murdoch

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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E-Mail: (Ted Harding) <ted.harding at wlandres.net>
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Date: 05-Jun-11                                       Time: 15:37:32
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