Why is M Poorly Conditioned?

• I note that in using this method, I got to look at values of the . It was not uncommon for

  

• You can ask why one gets such large ratios.

• Intuitively, the eigenvectors of M with small eigenvalue correspond to linear combinations of that are badly determined.

• So very small 's say that your theoretical formalism is redundant or alternatively the data inadequate.

• For instance, in fitting a cross section to

  then often the coefficients of the higher order Legendre functions are poorly determined, and

  if you choose n to be ``too big,'' then small eigenvalues will develop.

• In this case, one can cure the problem by reducing the top index n but in general no such simple solution exists.