Hey, I have what I feel is a true newbie question here:

I'm trying to work through an example calculating a singular value decomposition in Matlab, in order to create a program doing it automatically to an arbitrary matrix. But I'm stumped at the very first step. I use a line on the form

[a b] = eig(A' * A);

to calculate eigenvectors/values; I then have a piece of code reversing the order of things so I have eigenvalues and vectors appear from greatest to least value. Here's the mystery:

The matrix in the example is

A = [4 11 14; 8 7 -2].

The eigenvectors I calculate agree with the example for vectors v1 and v3, but in v2 it flips the signs on the entries. According to the book it should be

[-2/3 -1/3 2/3],

while I get

[2/3 1/3 -2/3].

What is going on here? Am I doing something blatantly silly? The example is lifted from David Lay's "Linear algebra and its applications", 3 ed chapter 7.4, if that's any use.

So yea, any insightful comment would be more than appreciated at this point!