I largely agree with your comments in this thread -- I'd been thinking about trying to express the same thing myself. I'd been guessing the motivation would be ML, where I feel that most people substantially overestimate how much they'd need.
Signals processing, though, is one of the places where I actually think a decent understanding of some of the higher-level concepts in linear algebra is really helpful. Linearity itself comes to mind, and maybe it just reflects my physicist's education, but it's hard for me to imagine having a working understanding of Fourier transforms without getting the idea of changing bases. I feel like you're about halfway through a first linear algebra course before you'd get there.
EDIT: that said, a good signals processing book probably covers a lot of this in sufficient depth if you can figure it out. The other catch-all comment I'd make is that linear algebra from a math class can look somewhat different from practical linear algebra on a computer. (That it's often a bad idea to directly invert a matrix for many computing applications is non-obvious from math class.) A book like Trefethen and Bau is great on that latter subject but is not a good starting point for OP.
Signals processing, though, is one of the places where I actually think a decent understanding of some of the higher-level concepts in linear algebra is really helpful. Linearity itself comes to mind, and maybe it just reflects my physicist's education, but it's hard for me to imagine having a working understanding of Fourier transforms without getting the idea of changing bases. I feel like you're about halfway through a first linear algebra course before you'd get there.
EDIT: that said, a good signals processing book probably covers a lot of this in sufficient depth if you can figure it out. The other catch-all comment I'd make is that linear algebra from a math class can look somewhat different from practical linear algebra on a computer. (That it's often a bad idea to directly invert a matrix for many computing applications is non-obvious from math class.) A book like Trefethen and Bau is great on that latter subject but is not a good starting point for OP.