singular value decomposition

(1.8 hours to learn)


The singular value decomposition is a factorization of a matrix A into three matrices UDV^T, where D is diagonal and U and V have orthonormal columns. It's closely related to the eigenvalues and eigenvectors of A^T A and A A^T. It gives a way of analyzing general matrices (not necessarily square) in terms of things somewhat analogous to eigenvalues. Common applications include latent semantic analysis (LSA) and principal component analysis (PCA), a dimensionality reduction algorithm.


This concept has the prerequisites:

Core resources (read/watch one of the following)


MIT Open Courseware: Linear Algebra (2011)
Videos for an introductory linear algebra course focusing on numerical methods.
Author: Gilbert Strang


See also