How to make an Eigenvector orthonormal?

Question

I am trying to figure out the PCA of a Data-set using calculation , and in one phase of this calculation I have the two eigenvectors :

$V_1=(\frac{1}{\sqrt2} , -\frac{1}{\sqrt2} ,0)t $ ; $V_2 = (0.32 , 0.32 , 0.88)t$

That I need to make orthonormal .

Q1: How to proceed ? Q2: Why should I do that to find the PCA ?

Thanks .

Answer 1

PCA is a symmetric process, so the eigenvectors will automatically be orthogonal. You just want to make sure the vectors are unit length, but it looks like they already are. So you are done.

For PCA, you want to have the eigenvectors with unit length so that length is preserved when you write a data point in terms of the eigenvectors.

Answer 2

Since they are orthogonal, divide them by their norm to make them orthonormal.

Q2 is a very good one. To find PCA you need the eigenvectors, which are generally not unit vectors - although they can be.