Linear Algebra and Its Applications · Problem 3.4.28
Orthogonality — Gilbert Strang
Mathematics · gram-schmidt-plane
Problem
Apply Gram-Schmidt to (1,−1,0), (0,1,−1), and (1,0,−1), to find an orthonormal basis on the plane x1+x2+x3=0. What is the dimension of this subspace, and how many nonzero vectors come out of Gram-Schmidt?