Finding a normalized eigenvector

[XSK]

ok, i know how to find an eigenvalue and an eigenvector that's fine, what i don't remember is how to normalize your eigenvectors

in my problem i have 2 eigenvectors, (1,3) and (3,1)

(1,3) corresponds to eigenvalue 10

(3,1) corresponds to eigenvalue 20

in my notes i have written 'to normalize make equal to one and solve', of course this was about a month ago and i have completely forgotten what i meant by that.

any help appreciated!

 

[nicksauce]

Usually, what is meant by "normalize" is to make the norm be 1, so you divide the vector by its length. Ie (1,3) normalized is (1, 3)/sqrt(10).

 

[jaderberg]

Yes to normalise the eigenvector the modulus has to equal 1. So it would be 1/sqrt(1^2 + 3^2) and 3/sqrt(10)