Gram Schmidt Process in Diagonalization

Question

I have to find a matrix P that orthogonally diagonalizes matrix A. where

A= 4 2 
   2 4

I have found the eigen values and eigen vectors.

first eigen value= 2
eigen vector is (-1,1)

second eigen value= 6
eigen vector is (1,1)

but i am stuck here as i dont know how to proceed further using Gram Schmidt process. Please help !

Answer 1

You have already found the eigenvectors and it turns out they are orthogonal. Now in order to find an orthonormal basis, you just have to divide the vectors by their norms. Then , you would get an orthonormal basis of vectors. The matrix can then be easily constructed.