One possible perspective: thinking of images as a vector space, and thinking of image operations like blurring, sharpening, and even any spatial transformation as linear operators (representable as matrices).
This perspective is most straightforward with a 1-dimensional domain, like an audio signal, or the temperature along a thin rod, because there's a clear way to organize all the values in a vector, e.g. all the audio samples are just in sequence. So if that's appealing to you at all, I would recommend that first. You can do filtering (like with an "equalizer") and add effects like echo/reverb as linear operations.
I think that it is particularly fun to think of some ground-truth signal that is corrupted by an echo in a room and a microphone that attenuates some frequencies, and trying to undo that corruption.
You could try making a simple software-rendered 3D game from scratch. Basic 3D rendering is pretty much all linear algebra computations involving matrices and vectors.
Check out “eigenfaces.” It’s straight forward and works reasonably well. There are a lot of interesting applications of PCA and SVD. Signal and noise separation, machine learning, the list goes on.
What are some fun projects that uses LA for an individual? I'm thinking about things like generative art, if anyone knows of any artists that inspire them.