My idea was not to build the best method for finding Eigenvalues and Eigenvectors, but to understand them. The trouble with using LAPACK without understanding is not the way to learn. Neither is studying LAPACK productive in that rather than understanding the theory all effort is spent learning how LAPACK avoids numerical approximations forced by the limited precision of computers.
I wanted to apply the method for calculating Eigenvalues as described in text books. Only use J notation instead of standard mathematical notation. As a side effect the result is a J script that can calculate Eigenvalues. It is will known that p. does not do well for large polynomials, but using p. allows one to follow the theory of Eigenvalues without getting bogged down on how to factor polynomials. What frustrated me was that I could not find any information on calculating Eigenvectors. So I posted my struggle to handle Eigenvectors looking for advice. I appreciate the help given to me so far. I have found Gilbert Strang's book and will read it. Also found this afternoon that Khan has lectures on Eigenvalues and Eigenvectors. I look forward to studying them. Personally I think that J can so closely match textbook mathematical notation is neat and its ability to do polynomial arithmetic so easily shows the unique power of J. On Sat, Feb 4, 2012 at 4:51 PM, Henry Rich <henryhr...@nc.rr.com> wrote: > Agreed, and note that solving the characteristic polynomial is NOT used > for finding eigenvalues of any but the smallest systems. *Numerical > Recipes*, which generally thinks that any citizen can write their own > code to do almost anything, suggests that you leave eigenvalues to LAPACK. > > Henry Rich > > On 2/3/2012 10:00 PM, Kip Murray wrote: > > For applications get a copy of Gilbert Strang's Introduction to Linear > > Algebra and read his Chapter 6 Eigenvalues and Eigenvectors. The bad > > news is, this chapter starts on page 274. You are expected to > > understand why he calls 2 2 $ 0.5 a projection matrix and 2 2 $ 0 1 1 0 > > a reflection matrix. The good news is, he never forgets applications, > > and his presentation of the math is first rate: "I try to explain rather > > than to deduce." You begin to respect eigenvalues and eigenvectors when > > you see their application to systems of differential equations in > > section 6.3. > > > > On 2/3/2012 5:03 PM, Don Guinn wrote: > >> > >> I would appreciate comments and suggestions and where to go to better > >> understand the applications of Eigenvalues and Eigenvectors. > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
