[eigenket]

There are (at least) two different things we're calling "linear algebra here", roughly speaking one is building the tools and one is using the tools.

The mathematicians need to understand the basics of of mathematical proofs to learn how to prove new interesting (and sometimes useful) stuff in linear algebra. You have to do the math stuff in order to come up with some new matrix decomposition or whatever.

The engineers/data scientists/whatever people just need to understand how to use them.

You don't need to know how to build a car to drive one. The mathematicians are building the cars, you're using them.