In the following, matrices will be indicated by indexed variables. "Subject" indices will be indicated using letters formula_22,formula_23 and formula_24, with values running from formula_25 to formula_26 which is equal to formula_27 in the above example. "Factor" indices will be indicated using letters formula_26, formula_29 and formula_30, with values running from formula_25 to formula_32 which is equal to formula_33 in the above example. "Instance" or "sample" indices will be indicated using letters formula_34,formula_35 and formula_32, with values running from formula_25 to formula_38. In the example above, if a sample of formula_39 students participated in the formula_40 exams, the formula_34th student's score for the formula_22th exam is given by formula_43. The purpose of factor analysis is to characterize the correlations between the variables formula_44 of which the formula_43 are a particular instance, or set of observations. In order for the variables to be on equal footing, they are normalized into standard scores formula_46: