The use of car data and how it correlates is a good way of showing how PCA treats each variable. For example acceleration and weight are negatively correlated while displacement and horsepower are highly correlated.
I'm sure it's still very popular in engineering. It's still very much the lingua franca for numerical methods applied to engineering problems - there are decades of materials solving engineering problems written in MATLAB.
Matlab is great. I won’t hire anyone who only has experience in it though, like I might hire someone who only has python numerical analysis tools experience. It’s brittle and difficult to put into production in my experience.
It's used heavily in school still. I think statistics and data science in general have dropped it along with other relics like SAS (used today only by those people who haven't bothered learning anything other than SAS), and are sticking with R and python for functionality previously done in matlab.
Yes. We made a proof on concept thing on top of a closed source 2.4Ghz radio wave propagation simulator built in matlab. Interfacing to compiled matlab through hacky command line and .mat files is a pretty horrifying experience :)