That said, "email" — "electronic mail" — pretty clearly conveys in its name what it's about.
If I hear the word "matrix" out of context I'm probably going to think of mathematics or material science or something else first. In other words, "matrix" is already an overloaded term, and its other meanings aren't going to go away any time soon.
Now "email" is synonymous with "Internet E-mail over SMTP" which was not always the case by any stretch of the imagination.
It used to be there were many systems/protocols and even self-hosted in isolation email systems and bulletin boards. Some still operate to this day, though mostly delivered over the internet, but through different channels than general SMTP internet email.
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That said, email is a better term than matrix, but any other term still wouldn't be the same meaning... "matrix protocol" vs "smtp" might be more narrow/accurate.
If I hear the word "matrix" out of context I'm probably going to think of mathematics or material science or something else first. In other words, "matrix" is already an overloaded term, and its other meanings aren't going to go away any time soon.