Very nice, you've impressed me with your linear algebra skills. Now what?
Just like in the classic VSM, to compare a query and a document in LSI we create vectors for each.
To create a vector for a bunch of words (query, document), we
simply add together the vectors for the words in the bunch. In VSM,
each term is represented by an n-dimensional unit vector. In LSI,
each term is represented by a k-dimensional vector: a row of
.
That's it. There's other mathy mumbo jumbo to justify pieces of this, but the nice thing about it is that it works quite nicely (circa late 80's).