Difference in goals between pca and fa, Applied Statistics

In PCA the eigknvalues must ultimately account for all of the variance. There is no probability,'no hypothesis, no test because strictly speaking PCA is not a statistical procedure. The PCA is merely a mathematical manipulation to recast m variables as m factors. Factor analysis (FA), however, brings a priori knowledge to the problem solving exercise.

'There is a short list of primary assumptions behind factor analysis. But basically. factor analysis assumes that there are  cowelations/covariances between the m variables in the datp set that are a result of p underlying, mutually uncorrelated factors.

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