Eigen vectors/values with LAMBDAs

Hi edugca,

Thank you for your reply! And sorry for the delay in response.

It was not until yesterday that I could have a look at the repertoire of formulae that you have developed, and I must say I am amazed! Congratulations on your terrific work!

That said, the EIGENVALUES() and EIGENVECTORS() formulas, as far as I could thest them, don't seem operative enough for my application (a matrix with dimension 18, and non-integral numbers -not sure if the latter could be causing trouble though). Most of the times, they do not produce all the eigenvalues/vectors (for a given set of parameters -eigenMin, eigenMax, eigenStep-, both produce the same number of eigenvectors as number of eigenvalues. But somehow they do not produce the full set, which R does). That's one big issue. The other issue is calc time, which can get very slow.

To tackle the first issue I tried playing with the eigenMin and eigenMax parameters to widen the interval the formulae sweep through; and with the eigenStep to make smaller increments, at the expense of performance, up to the point where runtime was clearly not viable (what I mean is, maybe there could be a smaller increment which would add way more steps and eventually produce the values/vectors, but I did not test thoroughly if runtime was already a no-go).

As far as I gathered from your lambda coding, the eigenvalues algorithm generates a vector of many candidates for eigenvalues. It then tests each one to see if they satisfy the characteristic equation

|A- candidate I | = 0. If it does, the candidate is an eigenvalue. But it goes beyond and also checks for sign changes in the LHS of the equation, as candidates are tested sequentially. In the event of a sign change, the candidate is regarded as an eigenvalue. I think I get the rationale, but for some reason it's not yielding all the eigenvalues.

I'll keep exploring it and upload an example file if still not successful.

Thanks!

Regards,

Diego