How do you find the killing vectors for Minkowski space?

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Homework Statement


How do you find the killing vectors for Minkowski space(or from any metric as well)?

Homework Equations

The Attempt at a Solution


I'm new to GR and I'm going through Carroll's book. I've been alright so far but for some reason I just don't understand what's going on here. Could you guys explain in detail or send me to an online lecture or something to help?
 
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If X^\mu is a killing vector field, then it obeys the equation:

\nabla_\alpha X_\beta + \nabla_\beta X_\alpha = 0

where \nabla_\alpha is the covariant derivative.
 
I seem to have forgotten notation. -.- I wasn't even thinking of the covariant derivative. Thanks haha
 
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