Orthogonal basis

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.^{[citation needed]}

References

Weisstein, Eric W., "Orthogonal Basis" from MathWorld.

This algebra-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Linear algebra Algebra stubs Wikimedia Foundation. 2010. Игры ⚽ Нужна курсовая? Orthogonal polarization spectral imaging Orthogonal diagonalization Look at other dictionaries: Basis (linear algebra) — Basis vector redirects here. For basis vector in the context of crystals, see crystal structure. For a more general concept in physics, see frame of reference. In linear algebra, a basis is a set of linearly independent vectors that, in a linear… …   Wikipedia Orthogonal group — Group theory Group theory …   Wikipedia Orthogonal diagonalization — In linear algebra, an orthogonal diagonalization of a square matrix is a diagonalization by means of an orthogonal change of coordinates. The following is an orthogonal diagonalization algorithm that diagonalizes a quadratic form q(x) on Rn by… …   Wikipedia orthogonal — adjective Etymology: Middle French, from Latin orthogonius, from Greek orthogōnios, from orth + gōnia angle more at gon Date: 1612 1. a. intersecting or lying at right angles b. having perpendicular slopes or tangents at the point of intersection …   New Collegiate Dictionary Orthogonal Defect Classification — (ODC) ist ein Modell zur Fehlerklassifikation in der Softwareentwicklung, das bei IBM entwickelt wurde. Durch die Klassifikation von Fehlern nach bestimmten Kategorien und Attributen lassen sich Zusammenhänge zwischen dem Entwicklungsprozess und… …   Deutsch Wikipedia Orthogonal coordinates — In mathematics, orthogonal coordinates are defined as a set of d coordinates q = (q1, q2, ..., qd) in which the coordinate surfaces all meet at right angles (note: superscripts are indices, not exponents). A coordinate surface for a particular… …   Wikipedia Orthogonal matrix — In linear algebra, an orthogonal matrix (less commonly called orthonormal matrix[1]), is a square matrix with real entries whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors). Equivalently, a matrix Q is orthogonal if… …   Wikipedia Orthogonal — Die Orthogonalität bezeichnet: in der Mathematik das Konzept des Senkrechtstehens und des rechten Winkels (daher die Benennung orthogonal aus dem Griechischen für rechtwinklig); in der Informatik die freie Kombinierbarkeit unabhängiger Konzepte… …   Deutsch Wikipedia Orthogonal frequency-division multiplexing — Passband modulation v · d · e Analog modulation AM · …   Wikipedia Orthogonal functions — In mathematics, two functions f and g are called orthogonal if their inner product is zero for f ≠ g. Whether or not two particular functions are orthogonal depends on how their inner product has been defined. A typical definition of an …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”