"Dimensions" in dimensional analysis are not the same thing as dimensions in linear algebra! I'm not sure what a scalar quantity with an infinite dimension woul

"Dimensions" in dimensional analysis are not the same thing as dimensions in linear algebra! I'm not sure what a scalar quantity with an infinite dimension would be. (To reiterate, the dimensions of dimensional analysis tell you how quantities scale under adjustment of our scale of measurement, so having infinite dimension would mean scaling infinitely quickly…?) That being said, I did try to connect infinite-dimensional problems with dimensional analysis in this post. Towards the end of my section on dimensions with complex powers, I applied dimensional analysis to the study of periodic signals and ended up arguing that (complex) Fourier basis elements can be thought of as dimensionful objects. I haven't seen dimensions used like this before, so I was hoping to earn the vote from fans of functional analysis ;)