A set of inequalities in factor analysis.

where y = [yl y~ " ' " y~]' has covariance mat r ix r and is uncorre la ted wi th z = [zl z2 . z~]' which has covar iance mat r ix A, so t h a t z¢ is uncorre la ted wi th zi , 1 < i _~ j < p. T h e variable y~ is called the common-fac tor c o m p o n e n t of x~ and var(y~) -1 -~ is the communa l i ty of x¢ while z~ is the specific fac tor of x~ and var(z~) = ~ is the uniqueness of x¢ . Le t p~ denote the mult iple-correlat ion coefficient of x,. wi th the remaining p -1 variables. Then