LookAt Matrix Question - when are they equivalent

Could you please confirm or deny the following statements which I think are true?

1) Two LookAt matrices

 glLookAt(eye, center1, up)

and

 glLookAt(eye, center2, up)

are equivalent if center1 - eye == k(center2 - eye) for some positive k.

2) Tho LookAt matrices are never equivalent if their eye vector is different.

are equivalent if center1 - eye == k(center2 - eye) for some positive k.

That is correct. The direction vector is calculated from center - eye, and then normalized, so the length doesn't matter if the direction is the same.

Beware though that there could be very slight numerical differences in the resulting matricies because of rounding. For all practical purposes though, the matricies are the same.