Matrix Factorization and Latent Semantic Indexing Background Diagonal decomposition: why/how Let U have the eigenvectors as columns: UHy...y Then, su can be written Thus su=UA, or U-lSU=4 And s=uaU-Matrix Factorization and Latent Semantic Indexing 11 Diagonal decomposition: why/how           U= v vn ... Let U have the eigenvectors as columns: 1                     =           =           = n SUSv vn v n vn v vn   ...... ...... 1 1 11 1 Then, SU can be written And S=UU–1. Thus SU=U, or U–1SU= Background