Replacing a submatrix of a matrix

Question

Minding the fact that

In[102]:= {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}[[1 ;; 2, 1 ;; 2]]

Out[102]= {{1, 2}, {4, 5}}

is the upper left submatrix.

I would like to do the following :

> helios = {{{3, 2}, {1, 2}}, {{3, 2}, {2, 1}}, {{3, 1}, {2, 2}}, {{1, 
>     3}, {2, 2}}, {{2, 3}, {1, 2}}, {{2, 3}, {2, 1}}, {{1, 2}, {3, 
>     2}}, {{2, 2}, {3, 1}}, {{2, 1}, {3, 2}}, {{2, 1}, {2, 3}}, {{1, 
>     2}, {2, 3}}, {{2, 2}, {1, 3}}}

ReplacePart[{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}, {1 ;; 2, 
     1 ;; 2} -> #] & /@ helios

That is, i would like to replace the upper left submatrix by a series of other matrices ! But this does not work as :

ReplacePart::pkspec1: The expression 1;;2 cannot be used as a part specification.

Does anyone have a efficient way of doing this ? with built-in functions if possible.

Thank you very much.

Answer 1

This is straight-forward to do with assignment:

m = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
m[[1 ;; 2, 1 ;; 2]] = {{3, 2}, {1, 2}};
m // MatrixForm

We can get the list of all matrices like this:

newMatrices = ConstantArray[m, Length[helios]];
newMatrices[[All, 1 ;; 2, 1 ;; 2]] = helios;