Dear Evans, John has given a good answer, but I thought I'd remark that I have seen this behaviour when creating doctests for numerical routines for matrices over RDF/CDF. It sometimes seems like this "unpredictable" sign change depends on the hardware in use (perhaps because different versions of underlying linear algebra libraries are in use). So not a bug, but an annoying fact-of-life. There is only so much mileage you can get from standardizing eigenvectors to norm 1.
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