Matrix Factorization and Latent Semantic Indexing Background Eigenvalues eigenvectors Eigenvectors (for a square m xm matrix s) Sy=Av Example 2 (right)eigenvector eigenvalue(4 0)(2, 2 ∈R≠0A∈R a How many eigenvalues are there at most? Sv=v<→(S-Av=0 only has a non-zero solution if $ -AI=0 This is a mth order equation in n which can have at most m distinct solutions (roots of the characteristic polynomial)-can be complex even though S is real.Matrix Factorization and Latent Semantic Indexing 4 Eigenvalues & Eigenvectors ▪ Eigenvectors (for a square mm matrix S) ▪ How many eigenvalues are there at most? only has a non-zero solution if This is a mth order equation in λ which can have at most m distinct solutions (roots of the characteristic polynomial) – can be complex even though S is real. (right) eigenvector eigenvalue Example Background