Eigenvectors

[parisse]

If you are a perpetual student, then you should at least consider my mathematical expertise and arguments before deciding that you are right and I'm wrong. Let me illustrate on this example that approx algorithms should not be the same as exact algorithms. Take for example a 30x30 random matrix a:=ranm(30,30). Compute the characteristic polynomial p:=charpoly(a). Of course you can not solve this polynomial exactly, but even in approx mode, look at the size of the coefficients, for example evalf(p[30]) and compare with the leading coefficient of p. How do you think one can compute the roots of this polynomial accurately? This is an ill-conditionned problem. And that's why numeric algorithms do not follow the same path as exact algorithms for eigenvalues/eigenvectors computation. This is also true for many other algorithms.