Incomplete Orthogonal Sets
Given a Hilbert space H and a set S of mutually orthogonal vectors in H, we can take the smallest closed linear subspace V of H containing S. Then S will be an orthogonal basis of V; which may of course be smaller than H itself, being an incomplete orthogonal set, or be H, when it is a complete orthogonal set.
Read more about this topic: Orthonormal Basis
Famous quotes containing the words incomplete and/or sets:
“I dont think there is anything on earth more wonderful than those wistful incomplete friendships one makes now and then in an hour’s talk. You never see the people again, but the lingering sense of their presence in the world is like the glow of an unseen city at night—makes you feel the teemingness of it all.”
—John Dos Passos (1896–1970)
“Whether changes in the sibling relationship during adolescence create long-term rifts that spill over into adulthood depends upon the ability of brothers and sisters to constantly redefine their connection. Siblings either learn to accept one another as independent individuals with their own sets of values and behaviors or cling to the shadow of the brother and sister they once knew.”
—Jane Mersky Leder (20th century)