Soon or later CS students, in particularly those in IR, will need to deal with similarity matrices.
In simple terms, any matrix M that exhibits the following five characteristics is a similarity matrix.
Squaredness = M must have the same number of rows and columns.
Non-Negativity = all elements of M must be real, non-negative numbers.
Boundedness = all elements of M must adopt values between 0 and 1.
Reflexivity = all diagonal elements of M (i.e. from left to bottom) must be filled with 1.
Symmetry = all ij elements must be identical to all ji elements.
A matrix that fails to exhibit any of these characteristics is not a similarity matrix.
Accordingly, some matrices found in the literature on LSI and whose elements have been referred to as similarities are not so since the corresponding matrix does not conform to the above definition.
Note. This information will help those that took the IR Quiz on Matrices to realize how well they did.