It's an ancient and likely irrevocable error, like "font" instead of "typeface" (no really, go look it up, we have all been saying "font" when the thing we're talking about is (well, was) "typeface". I only know this because Woz used to tilt against this particular windmill.)

Jef Raskin pointed out years ago in his "Humane Interface" that in UI when we say "intuitive" we really mean just "familiar".

His example was the computer mouse. He gave one to an architect (buildings not software) friend and they turned it upside down and used it like a little trackball with their fingertip. (Raskin is that old mice were new.) Few read or heed Raskin.

Intuition is a vehicle for understanding. "Determinant says how much the matrix stretches things if treated like a function" is an intuition but doesn't give full understanding of the determinant.

Because I still don't pretend to fully understand linear algebra. But it's not a mystification anymore, thus "intuition".

"Intuition is the ability to acquire knowledge, without recourse to conscious reasoning or needing an explanation." https://en.wikipedia.org/wiki/Intuition

I don't think this is what you meant to say - have a partial understanding of something is not the same thing as intuition which is more like a "gut feeling".

> intuition which is more like a "gut feeling".

That's what I meant.

I don't know whether approaching linear algebra using a "gut feeling" approach is a good idea though.