Matrix Factorization and Latent Semantic Indexing Background Example Let 2 Real, symmetric 2- Then s-n= 12-2 S-A|=(2-1)2-1=0 The eigenvalues are 1 and 3 (nonnegative, real The eigenvectors are orthogonal (and real Plug in these values and solve for eigenvectorsMatrix Factorization and Latent Semantic Indexing 9 Plug in these values and solve for eigenvectors. Example ▪ Let ▪ Then ▪ The eigenvalues are 1 and 3 (nonnegative, real). ▪ The eigenvectors are orthogonal (and real):       = 1 2 2 1 S | | (2 ) 1 0. 1 2 2 1 2 − = − − =        − − − =      S I S I         − 1 1         1 1 Real, symmetric. Background