Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
1996
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1996

[Date Index] [Thread Index] [Author Index]

Search the Archive

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] ====


  • Prev by Date: Re: Numerical Differentiation
  • Next by Date: Re: Numerical Differentiation
  • Previous by thread: Re: Abs and variables
  • Next by thread: BarChart3D styles