Matrix Factorization and Latent Semantic Indexing Background Matrix vector multiplication Thus a matrix-vector multiplication such as Sx s, x as in the previous slide can be rewritten in terms of the eigenvalues/vectors. Sx=S(2v1+42+6v3) Sx=2Sv1+4S2+6S3=21v1+42+63 Sx=60v1+80v2+6v 3 Even though x is an arbitrary vector the action of s on x is determined by the eigenvalues/vectorsMatrix Factorization and Latent Semantic Indexing 6 Matrix vector multiplication ▪ Thus a matrix-vector multiplication such as Sx (S, x as in the previous slide) can be rewritten in terms of the eigenvalues/vectors: ▪ Even though x is an arbitrary vector, the action of S on x is determined by the eigenvalues/vectors.  Sx = S(2v1 + 4v2 + 6v 3 ) Sx = 2Sv1 + 4Sv2 + 6Sv 3 = 21 v1 + 42 v2 + 6 3 v 3 Sx = 60v1 + 80v2 + 6v 3 Background