about matrices merge and retrieve algorithm.

I have a problem as follows:

 1. If we have 3 matrices A,B,C and we merge them in a single matrix ABC by
any method like addition , subtraction division,multiplication,etc
 2. and then we want to retrieve original 3 matrices A,B,C from single ABC
matrix
What will be the algorithm?

Hello.

Note that the above operations lose information. For example, if

  A <- matrix(2, nrow=2, ncol=2)
  B <- diag(2)
  C <- B[2:1, ]
  ABC <- A + B + C
  ABC
  #      [,1] [,2]
  # [1,]    3    3
  # [2,]    3    3

then ABC does not contain enough information to reconstruct the
original A, B, C.

If you want to get any three matrices A, B, C, whose sum is ABC,
then choose any two matrices A, B and compute C as ABC - A - B.

If it is known that the original matrices are not arbitrary and
satisfy some property, which allows to find a unique solution, then
the algorithm depends on what is known about the original matrices.

Hope this helps.

Petr Savicky.