Gram-Schmidt Procedure

If you have linearly independent vectors and want to convert them into an orthonormal Set, you can follow the Gram-Schmidt procedure.

Given $v_1,v_2,…,v_n$ as LI Vector, then $u_1, u_2, …, u_n$ can be built using

This makes $u$ an orthogonal vector

Then you normalize $u$ to get a orthonormal vector. You do this by multiplying the Magnitude of the vector.