Eigenvectors results query

Could someone explain this result. The eigenvectors seem wrong. a simple hand computation yields {1,1} as the eigenvector associated with the eigenvalue 1 and {1,-2} for the eigenvector associated with eigenvalue .7

what you obtained by hand computation is wrong. Try this and you will see

A . {1, 1}
A . {1, -2}

The eigenvector for the eigenvalue .7 is {1, -1}, not {1,-2}.

point taken, but what about the Mathematica output ?

they are the same, only a normalization factor difference

Ahh, thank you,