Normalize Vector: Steps & Solutions

[Roni1985]

Homework Statement

Normalize the 1xn vector

v=<c,c,c...c>

Homework Equations

U=V/|V|

The Attempt at a Solution

I have a solution to a different question and it says this:
if each element is c, we can normalize it and divide it by the sum of the elements.
So, what they did was
c/(n*c)=1/n

As far as I remember, it needs to be 1/(sqrt(n))

Or, there are different methods to normalize vectors?Thanks.

 

[fzero]

Homework Statement

Normalize the 1xn vector

v=<c,c,c...c>

Homework Equations

U=V/|V|

The Attempt at a Solution

I have a solution to a different question and it says this:
if each element is c, we can normalize it and divide it by the sum of the elements.

You actually have to divide by the square root of the sum of the squares of the elements.

So, what they did was
c/(n*c)=1/n

As far as I remember, it needs to be 1/(sqrt(n))

Or, there are different methods to normalize vectors?

There aren't really different methods, but it's possible to carry out some calculations in different ways.

First of all, the way that will always work is to just explicitly compute |v| and use the definition of the normalized vector u = v/|v|. In this specific case, v = <c,...,c> = c <1,...,1> by the rules of scalar multiplication, so we can instead just divide by c right here and normalize <1,...,1>.

You seem to be on the right track (your comment about the square root is important), but it's probably worthwhile to just do the calculation explicitly instead of trying to reproduce an example in your notes.

 

[Roni1985]

You actually have to divide by the square root of the sum of the squares of the elements.



There aren't really different methods, but it's possible to carry out some calculations in different ways.

First of all, the way that will always work is to just explicitly compute |v| and use the definition of the normalized vector u = v/|v|. In this specific case, v = <c,...,c> = c <1,...,1> by the rules of scalar multiplication, so we can instead just divide by c right here and normalize <1,...,1>.

You seem to be on the right track (your comment about the square root is important), but it's probably worthwhile to just do the calculation explicitly instead of trying to reproduce an example in your notes.

I see, thanks for your answer. It was very helpful.