By Andrew Ng's lecture notes (which you can find at http://cs229.stanford.edu/notes2020spring/cs229-notes9.pdf), the factor analysis model has the following structure:
Written out mathematically like this, it's quite obvious that we are trying to estimate the density function of random variable $x$.
However, I find it difficult to connect the math (especially the matrices $\mu$, $\Lambda$ and $\Phi$) with how factor analysis is used in practice to discover "important latent variables". Can someone elaborate this connection a bit more? In particular, what further analysis do we perform with these matrices?