The term on the left is the formula_76-term of the correlation matrix (a formula_77 matrix derived as the product of the formula_78 matrix of standardized observations with its transpose) of the observed data, and its formula_26 diagonal elements will be formula_25s. The second term on the right will be a diagonal matrix with terms less than unity. The first term on the right is the "reduced correlation matrix" and will be equal to the correlation matrix except for its diagonal values which will be less than unity. These diagonal elements of the reduced correlation matrix are called "communalities" (which represent the fraction of the variance in the observed variable that is accounted for by the factors):