I meant a "transform" as a linear map. I'm using the word as it is used in computer graphics (my background), so it's something that translates, rotates, scales, etc. other things (such as points). That is often a 3x3 or 4x4 matrix, although it can also be a vec3 translation and a quaternion, or just a quaternion. I think "Transform" is clear in the context of computer graphics, but I see what you mean about it being vaguely defined in my blog post.
In robotics, it's pretty widely used to refer to a 6-degree of freedom pose or relative pose in space, for example it's widely used in ROS, a de facto standard https://docs.ros.org/en/melodic/api/geometry_msgs/html/msg/T.... Not sure if there they're just using it as an example in the graphics.
I read their previous post, and nowhere do they explicitly say "a transform is a...". One might assume that it is indeed a linear transformation, as you suggest, but it shouldn't be up to the reader to do detective work just to understand the objects the author is talking about.
What I meant was that based on what they said in their previous post ("[g]iven a transform T and a point x, we can find the transformed point with T∗x") and the interactive graphics, I felt certain they meant a linear map.
I agree it's sloppy, at least a reference or something should be given if one doesn't want to spend time on the full definition.
Maybe the author could have used a more general notion, then, if omission and brevity were going to be present? Like, instead of a linear map or transform, he could have said an operator or something.
I don't know what is the general form of a transform or linear map. I think it's something like operator, though.
True, however I don't know how well versed the author is. Back in my late teens when I was deep into 3D graphics and ray tracing, I knew a lot about that specific math but not much beyond it. To me, "transform" was crystal clear to mean some kind of linear transform, and I hadn't yet learned of the more general operator notion[1].
So I can see myself writing something similar thinking it was clear.