[mrfox321]

Re [1]: it's fairly concrete to simply say that matrix multiplication can be performed block-wise.

[PartiallyTyped]

I don’t disagree; but that is just an example of MM. The gist is not that you can do block multiplication; but that you can define matrices over any non commutative ring, which includes other matrices - ie blocks.

[mrfox321]

Yeah matrices are more abstract. I guess I am just pointing out that your concrete example of non-commutative rings (matrices of matrices) still needs a proof to demonstrate bijection between 4N x 4N (scalar) and 4 x 4 (N x N(scalar)).

Block MM demonstrates the equivalence.