Counting Elements in Hom(V,W) for Finite Linear Transformations

JaysFan31

Homework Statement


The set Hom(V,W) is the collection of all linear transformations from the F-space V to the F-space W. Suppose that F,V, and W are all finite. Suppose that F=Zp for some prime p, that V is n-dimensional over F, and W is n-dimensional over F. How many elements does Hom(V,W) have?

Homework Equations


Nothing.

The Attempt at a Solution


I'm pretty sure it's p^n.

I have the proof of dimV=m and dimU=n meaning dimHom(V,U)=mn. How do I transform this proof to the one I want?
 
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Would the answer still just be n^2?
 

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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