Also found in: Dictionary, Thesaurus, Medical, Wikipedia.


Two geometric objects have this property if they are perpendicular.



a generalization and often a synonym of the concept of perpendicularity. If two vectors in three-dimensional space are perpendicular, their scalar product is equal to zero. This fact permits us to generalize the concept of perpendicularity by extending it to vectors in any linear space, where a scalar product is defined with the usual properties. Thus two vectors are said to be orthogonal if their scalar product is equal to zero. In particular, let us define the scalar product in the space of complex-valued functions on the interval [a, b] by the formula

where ρ(x) ≥ 0. Then, if (f, ϕ)ρ = 0, that is,

f(x) and ϕ(x) are said to be orthogonal with respect to the weight function ρ(x). Two linear subspaces are termed orthogonal if every vector in one of them is orthogonal to every vector in the other. This concept generalizes the concept of the perpendicularity of two lines or of a line and a plane in three-dimensional space but not the concept of the perpendicularity of two planes. Curves that intersect at right angles, as measured by the angle between the tangents at the point of intersection, are called orthogonal curves.

References in periodicals archive ?
When more than one variable from the information set is used as an instrumental variable in estimation, the model is overidentified and a J-test can be used to test the orthogonality condition.
In this paper we present the orthogonality relation based method for post-processing FE predictions in order to separate Lamb modes at a plate edge in the plane strain condition.
The trivial orthogonality on a vector space [Laplace] defined by (i), and for nonzero elements x, y [member of] [Laplace], x [perpendicular to] y iff x, y are linearly independent.
where the absolute value of the scalar multiplication of vectors e describes the degree of orthogonality (true orthogonality cannot be reached for the time series of financial markets).
Urn A [] Urn C TABLE A1 Verification of Orthogonality of Assignments to Treatments to Data from First Experiment Means Received Received Ambiguous Detailed Payout Payout Full E-mail E-mail Sample Solicitation Solicitation (1) (2) (3) More ambiguity 0.
In this paper, we introduce new definitions of orthogonality using theory of best approximation in Banach spaces and projections on subspaces in Banach spaces.
p] provides one more orthogonality relation [30, 31], namely
Wavelet OFDM reduces the side-lobe level of each subcarrier with no redundant signals as a result of setting the orthogonality of the wave-frequency domain and time domain.
They are based on observation that a strict WDO assumption (disjoint orthogonality of sources in the frequency doimain) is practically not fully satisfied.
We use the generalized orthogonality principle to tune the forecaster parameters.
Design orthogonality ensures that the attribute levels are uncorrelated, permitting estimation of the statistical model (Hensher et al.

Full browser ?