Re: What's behind PseudoInverse

*To*: mathgroup at smc.vnet.net*Subject*: [mg4332] Re: What's behind PseudoInverse*From*: richard at seuss.math.wright.edu (Richard Mercer)*Date*: Thu, 11 Jul 1996 00:57:43 -0400*Organization*: Wright State University*Sender*: owner-wri-mathgroup at wolfram.com

In <4q5kak$bsb at dragonfly.wolfram.com> Lorenzo Flueckiger wrote: > Hello, > > The Mathematica function "PseudoInverse" do exactly what I need (for > inversion of rectangular numerical matrices)... But how it really works? > Does anybody know where I can find some documentation (method used or > algorithm or equivalent package in C or ...) about this "magic" > function? > > Thanks in advance > > Lorenzo > There is a short but good discussion of pseudoinverses in Gil Strang's "Introduction to Linear Algebra". I suggest that you look carefully at it or similar account of this topic; I do not think it makes sense to use pseudoinverses without understanding them. Very briefly, it is based on the "singular value decomposition" of a matrix, which is a generalization to arbitrary matrices of the diagonalization of a symmetric square matrix. One uses the square roots of the eigenvalues of A*A to create a diagonal matrix S, and orthogonal matrices U and V to write A = USV' (where the apostrophe means transpose). Replacing S by its easily found inverse then results in the pseudoinverse of A. -- Richard Mercer richard at seuss.math.wright.edu "I meant what I said and I said what I meant, An elephant's faithful, one hundred per cent." ==== [MESSAGE SEPARATOR] ====