# Linear Discriminant Analysis Assumptions

I'm trying to learn about LDA and so i'm gathering information from different places. One thing which strikes me is on some occasions it's been explained that $\pi_{k}f_{k}(X=x)$ is normally distributed and that there are assumptions on the distribution of the data. From what i've seen these sources don't really dive deep into the geometry of dimensionality reduction. In other cases it seems that LDA is more of just an exercise in dimensionality reduction and there is very little that goes into explaining the underlying assumptions of distributions of the data. What is the 'correct' approach? Does anyone have a source which explains both? Often i can only seem to find an explanation detailing one approach.