Yes, this is correct; this phrasing was misleading. IMO, the most succinct formally correct characterization of similarities is:
As a map f:Rn→Rn, a similarity of ratio r takes the form f(x):=rAx+t, where A∈On(R) is an n×n orthogonal matrix and t∈Rn is a translation vector.
The only difference compared to congruence is that congruence requires r=1.
Yes, this is correct; this phrasing was misleading. IMO, the most succinct formally correct characterization of similarities is:
The only difference compared to congruence is that congruence requires r=1.