Matrix Factorization and Latent Semantic Indexing Background Matrix-vector multiplication 3000 S=0200 has eigenvalues 30, 20, 1 with corresponding eigenvectors 001 On each eigenvector, S acts as a multiple of the identity matrix: but as a different multiple on each Any vector(say X= 1)can be viewed as a combination of the eigenvectors X=2v1+4v+6vMatrix Factorization and Latent Semantic Indexing 5 Matrix-vector multiplication           = 0 0 1 0 20 0 30 0 0 S has eigenvalues 30, 20, 1 with corresponding eigenvectors           = 0 0 1 1 v           = 0 1 0 2 v           = 1 0 0 3 v On each eigenvector, S acts as a multiple of the identity matrix: but as a different multiple on each. Any vector (say x= ) can be viewed as a combination of the eigenvectors: x = 2v1 + 4v2 + 6v3           6 4 2 Background