How can I tell `Dot` to behave automatically linear?

Question

I would like the number $a$ to be taken out:

$Assumptions = (a) \[Element] Complexes && (X) \[Element] 
    Matrices[{n, n}];

(a X).(a IdentityMatrix[n]) // FullSimplify

Is there a way to make this product to yield $a^2 X$ instead of (X a).(a IdentityMatrix[n])? And to simplify the IdentityMatrix[n] as well?

P.S. Mathematica 10.

score 8 · Accepted Answer · answered Jun 02 '20 at 11:13

8

Use TensorExpand[] instead:

Assuming[a ∈ Complexes && X ∈ Matrices[{n, n}], 
         TensorExpand[(a X).(a IdentityMatrix[n])]]
   a^2 X

answered Jun 02 '20 at 11:13

1 Answers1