Explain how to do this in simple terms ?

this is an example of factor analysis

 

Example => Say X (X1, X2, X12) p= 12 and say a factor model with q 2 is appropriate. has 12(12+1)/2 = 78 elements. A has 12 x 2 = 24 elements. has 12 elements. This implies 24+ 12 = 36 elements in total for factor model. Problem! Most covariance matrices cannot be uniquely factored as A A+ when q < < p.