So I am trying to derive the following relation using Cauchy Schwarz inequality for any collection of N real numbers:
This says that the square of the average is less or equal than the average of the squares.
So I want to use to derive this.
So needs to be therefore, I have as and as providing that:
{1}{N}" alt="{1}{N}" />
Am I going in the right direction? Can anyone provide me some guidance?
I do apologise, it was a typo on my end and I forgot to add that I was using 1/N n amount of times.
But was my calculation of dot product incorrect then?
If you choose and , then those are real numbers. So, yes, your calculation of is incorrect, but your calculation of was correct. You would get . You cannot take it times because you chose to be a real number, not a number repeated times.