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I’m glad you like the idea. That was a good catch that I didn’t capture of the true meaning of linear very well. I was a little rushed before. That said, your definition isn’t correct either. Though it is true that linear functions have that property, that is merely the additivity property of a linear function which is just the distributive property of multiplication used on a polynomial. I also didn’t see where the linked text you provided even defines linearity or contains the additivity rule you listed. That was a linear algebra textbook chapter though, and I am still glad you showed me it because it reminded me of how I was great at math in college, but not at all because of the textbooks (which were very expensive!). I have rather good reading comprehension and college math textbooks might as well be written in another language. I learned the math 100% from the lectures and used the text books only to do the problems in the back and got an A in all 3 Calculus classes I took. I am pretty sure I could write a much easier to understand math textbook and I know it is possible because the software that teaches math isn’t nearly as confusingly worded as the textbooks.
This is how I would keep it as simple as possible and capture more of the original meaning:
Multiplying grids of numbers is a straight-line property process.
That said, point taken regarding math jargon being very challenging to descriptively reword as I suspect it will get a lot harder as the concepts get more complex. The point in my process isn’t to perfectly define the word but to use a descriptive enough word replacement that one’s brain more easily grabs onto it than it does with, for example, Latin terms of absurd length for anatomy like “serratus posterior inferior” which is a muscle I had trouble with recently. Just off the top of my head, I would just call that the lower ribcage stabilizer instead. That gives one a much better idea of where it is and what it does and would be much easier to remember and accurately label on a diagram for a quiz. However, with such abstract concepts like math deals with, this will certainly be very challenging.