Eigenvector Question: Is v=(2,1) the same as v=(4,2)?

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If I find a given eigenvector , that vector spans the entire eigenspace defined by that eigenvalue correct? Let's say I get v=(2,1) as an eigenvector. That is the same as saying v=(4,2) right? since they are spanning the same space?
 
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yes that is correct
 
thanks a lot
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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