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:
“Each of us is incomplete compared to someone else, an animal’s incomplete compared to a person ... and a person compared to God, who is complete only to be imaginary.”
—Georges Bataille (1897–1962)
“Almsgiving tends to perpetuate poverty; aid does away with it once and for all. Almsgiving leaves a man just where he was before. Aid restores him to society as an individual worthy of all respect and not as a man with a grievance. Almsgiving is the generosity of the rich; social aid levels up social inequalities. Charity separates the rich from the poor; aid raises the needy and sets him on the same level with the rich.”
—Eva Perón (1919–1952)