One of the ways to parallelize a problem is through data decomposition. Imagine a situation in which the task is to multiply a 2 x 2 matrix, which we will call Matrix A, by a scalar value of 4. In a sequential system, we will perform each multiplication operation one after the other, generating the final result at the end of all the instructions. Depending on the size of Matrix A, the sequential solution of the problem may be time consuming. However, when decomposition of data is applied, we can picture a scenario in which Matrix A is broken into pieces, and these pieces are associated with the workers that process the received data in a parallel way. The following diagram illustrates the concept of data decomposition applied to the example of a 2 x 2 matrix multiplied by a scalar value:

Data decomposition in a matrix example

The matrix problem presented in the preceding diagram had a certain symmetry where each necessary operation to get to the final result was executed...