Abstract Algebra: Schwarz Inequality Homework

icystrike
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Homework Statement


This is part of the proof of Schwarz inequity.
Please help me understand the following equation , i think it should not be a equal sign instead it should be greater or equal to.

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Homework Equations





The Attempt at a Solution

 

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will someone clear my doubt ? thanks in advance
 
No - the equals is correct. The norm is taken by multiplying out using the dot product (so a x b = aTb).
 
mrbohn1 said:
No - the equals is correct. The norm is taken by multiplying out using the dot product (so a x b = aTb).

Thanks mrbohn. (:
 

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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