Matrix Factorization and Latent Semantic Indexing Background Symmetric eigen decomposition If ErA is a symmetric matrix Theorem: There exists a(unique) eigen decomposition EM where Q is orthogonal: Q=Q Columns of Q are normalized eigenvectors Columns are orthogonal (everything is real)Matrix Factorization and Latent Semantic Indexing 14 ▪ If is a symmetric matrix: ▪ Theorem: There exists a (unique) eigen decomposition ▪ where Q is orthogonal: ▪ Q-1= QT ▪ Columns of Q are normalized eigenvectors ▪ Columns are orthogonal. ▪ (everything is real) Symmetric Eigen Decomposition S=QQ T Background