Yes, the Big Five were found by factor analysis, generally the PCA, which is basically an eigenvalue (spectral) decomposition of the (symmetric positive definite) covariance matrix of the data, which coincides with the SVD of the (normalised) data matrix.

The SVD is everywhere. IIRC, the first Netflix price was one won with the SVD:

https://en.wikipedia.org/wiki/Netflix_Prize

https://cseweb.ucsd.edu/classes/fa17/cse291-b/reading/Progre...