We will construct the ui's inductively so that fu1; ; ukg are orthonormal and Span(u1; ; uk) = Span(v1; ; vk) for Here we will learn a process for constructing an orthonormal basis for subspace W of Rm. Starting from any basis fv1; ;vng for W we construct an orthonormal basis fu1; ;ung. Gram–Schmidt Process: The process of forming an orthogonal sequence fykg from a linearly independent sequence fxkg of members of an inner-product space. Nonzero vectors v1, v2,, vk ∈ V form an orthogonal set if t