The Gram-Schmidt process is an algorithm used to convert a set of linearly independent vectors into an orthonormal set (a set of orthogonal, unit vectors).

Given a basis \(\{v_1, v_2, ..., v_k\}\), the process is as follows:

1. Step 1: Find the first orthogonal vector \(u_1\).
   \(u_1 = v_1\)
2. Step 2: Find the second orthogonal vector \(u_2\).
   \(u_2 = v_2 - \text{proj}_{u_1}(v_2)\)
3. Step 3: Find the third orthogonal vector \(u_3\).
   \(u_3 = v_3 - \text{proj}_{u_1}(v_3) - \text{proj}_{u_2}(v_3)\)
4. ...and so on for all vectors.

The projection formula is: \(\text{proj}_{u}(v) = \frac{v \cdot u}{u \cdot u} u\)

After finding each orthogonal vector \(u_i\), it is normalized to create the orthonormal vector \(e_i\):
\(e_i = \frac{u_i}{\|u_i\|}\)