The beauty about having orthonormal matrix is that it makes matrix computation trivial, and matrix computation is widely needed in all sorts of applications. So learn great deal from Dr.Strang’s course again here.

For example, projection

For example, least square problem is reduced to easy

So Gram-Schmidt is to come up with the approach to convert any independent matrix to orthonormal matrix.

A can be written as LU, here it’s QR. There is a practice problem: