Number of Roots
Till now, we have assumed that there is only one set of weights (weighted sum) that can be extracted from the two sets of variables. However, suppose that we had among our work satisfaction items particular questions regarding satisfaction with pay, and questions pertaining to satisfaction with one's social relationships with other employees. It is possible that the pay satisfaction items correlate with satisfaction with one's finances, and that the social relationship satisfaction items correlate with the reported satisfaction with one's spouse. If so, we should really derive two weighted sums to reflect this "complexity" in the structure of satisfaction.
In fact, the computations involved in canonical correlation analysis will lead to more than one set of weighted sums. To be precise, the number of roots extracted by the program will be equal to the minimum number of variables in either set. For example, if we have three work satisfaction items and seven general satisfaction items, then the program will extract exactly three canonical roots.