Matrix Factorization and Latent Semantic Indexing Background Eigen/diagonal Decomposition etsEra be a square matrix with m linearly independent eigenvectors a"non-defective"matrix) Theorem: Exists an eigen decomposition Unique diagonal for S= UAU distinct (cf. matrix diagonalization theorem) eigen values Columns of u are eigenvectors of S Diagonal elements of a are eigenvalues of s A=diag(入1,…,Mm),A2≥入2+1Matrix Factorization and Latent Semantic Indexing 10 ▪ Let be a square matrix with m linearly independent eigenvectors (a “non-defective” matrix) ▪ Theorem: Exists an eigen decomposition ▪ (cf. matrix diagonalization theorem) ▪ Columns of U are eigenvectors of S ▪ Diagonal elements of are eigenvalues of Eigen/diagonal Decomposition diagonal Unique for distinct eigen￾values Background