Basic Row Traversal Question

Right now I'm using this For loop to do an operation to each row of a $n \times n$ matrix, I was trying to figure out how to do this with Map or Take or something like that.

evecs = RandomReal[1, {5, 5}]
For[{i, 1, Length@evecs}, i++, evecs[[i, All]] = evecs[[i, All]]/Norm[evecs[[i, All]]]];

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Code doesn't run as-is. For[i=1,Length@evecs,i++... –  Corey Kelly Jun 24 '13 at 16:38
@CoreyKelly yes youre right, haha what is wrong? –  AimForClarity Jun 24 '13 at 16:39
Is this what you want ? evecs2 = #/Norm[#] & /@ evecs –  Emy Jun 24 '13 at 16:40
@Emy oh that was silly, /@ already takes the rows it doesnt map to each element of the array, i think that is where i got confused. Thanks that is it, but i still wonder why the for loop doesnt work? –  AimForClarity Jun 24 '13 at 16:41
Normalize /@ evecs –  Corey Kelly Jun 24 '13 at 16:41

#/Norm[#] & /@ evecs
As CoreyKelly pointed out though, in your case you are just normalizing the elements, so you can apply the Normalize function :
Normalize /@ evecs