I always thought that a submatrix is a contiguous part of a matrix. Like
as shown in http://mathworld.wolfram.com/Submatrix.html.
However in https://en.wikipedia.org/wiki/Matrix_(mathematics)#Submatrix there is a different definition: take any number of rows and columns away and the result is a submatrix:
This version will allow non-contiguous regions to be part of the submatrix.