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:
“Painting dissolves the forms at its command, or tends to; it melts them into color. Drawing, on the other hand, goes about resolving forms, giving edge and essence to things. To see shapes clearly, one outlines them—whether on paper or in the mind. Therefore, Michelangelo, a profoundly cultivated man, called drawing the basis of all knowledge whatsoever.”
—Alexander Eliot (b. 1919)