Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Math Background Matrices Singular Value Decomposition  
See also: Matrix Inversion, Eigenvectors and Eigenvalues  Advanced Discussion, The NIPALS Algorithm  
Singular Value DecompositionWhen trying to solve linear equation systems which are singular or "near singular" by Gaussian elimination or by LU decomposition these methods fail, or result in unstable solutions. In such cases the solution can be found by a method called singular value decomposition (SVD). SVD is based on the theorem of linear algebra which states that a matrix A (m columns, n rows) can be transformed into a product of three matrices U, W, and V^{T} which have specific properties: (1) the matrices U and V have orthonormal columns, (2) the matric V is quadratic, (3) the matrix W is a diagonal matrix with all nondiagonal elements equal to zero. 

Home Math Background Matrices Singular Value Decomposition 