I want to use Mathematica to show that the inner product of a vector with itself is equal to the square of its norm.
This is what I tried:
$Assumptions = x ∈ Vectors[3, Reals]; expr = Dot[x, x] == Norm[x]^2; FullSimplify[expr] (*x.x == Norm[x]^2*) TensorReduce[expr] (*x.x == Norm[x]^2*)
I had expected at least one of the last two lines to return
Why couldn't Mathematica simplify
True in this case? Are there additional assumptions I should include so that it return