Gram-Schmidt and the Legendre Polynomials of Small Degree

We apply the Gram-Schmidt algorithm to the set of polynomials {1, x ,x^2} with respect to the standard inner product on the space of continuous functions on [-1,1]. The orthogonalization procedure results in the first three Legendre polynomials (up to a normalization). These polynomials occur in many partial differential equations as we will see if further videos. #mikethemathematician, #mikedabkowski, #profdabkowski