In mathematics, particularly linear algebra, an orthogonal basis for an inner product space V is a basis for V whose vectors are mutually orthogonal. If the vectors of an orthogonal basis are normalized, the resulting basis is an orthonormal basis.
In functional analysis, an orthogonal basis is any basis obtained from a orthonormal basis (or Hilbert basis) using multiplication by nonzero scalars.
Any orthogonal basis can be used to define a system of orthogonal coordinates.
A linear combination of orthogonal basis can be used to reach any point in the vector space.
Famous quotes containing the word basis:
“Self-alienation is the source of all degradation as well as, on the contrary, the basis of all true elevation. The first step will be a look inward, an isolating contemplation of our self. Whoever remains standing here proceeds only halfway. The second step must be an active look outward, an autonomous, determined observation of the outer world.”
—Novalis [Friedrich Von Hardenberg] (1772–1801)