This table explains what we mean by a similarity measure. A similarity measure is a measure that loops overall ratings made by two users, and returns a score based on the sum of rating comparisons, distinguishing 4 cases:
Case 1: 	User-X and User-Y both rated Item-I.
	Case 2: 	User-X rated Item-I, but User-Y did not.
Case 3:	User-X did not rate Item-I, but User-Y did.
	Case 4:	Neither User-X nor User-Y rated Item-I.

This can be simplified using vector notation as following:
X * Y, where * indicates the special dot product between X and Y, with augmented arithmetic to deal with vectors that contain null values (to indicate that a user did not rate a particular item).