Orthogonality occurs when two things can vary independently, they are uncorrelated, or they are perpendicular.

In mathematics, two vectors are orthogonal if they are perpendicular, i.e., they form a right angle.

Definitions

Euclidean vector spaces

In 2- or higher-dimensional Euclidean space, two vectors are orthogonal if their dot product is zero, i.e. they make an angle of 90° or π/2 radians. Hence orthogonality of vectors is an extension of the concept of perpendicular vectors into higher-dimensional spaces. In terms of Euclidean subspaces, the orthogonal complement of a line is the plane perpendicular to it, and vice versa. Note however that there is no correspondence with regards to perpendicular planes, because vectors in subspaces start from the origin. (Our solved example in mathguru.com uses this concept)

Examples

The vectors (1, 3, 2), (3, −1, 0), (1/3, 1, −5/3) are orthogonal to each other, since (1)(3) + (3)(−1) + (2)(0) = 0, (3)(1/3) + (−1)(1) + (0)(−5/3) = 0, and (1)(1/3) + (3)(1) + (2)(−5/3) = 0.

http://en.wikipedia.org/wiki/Orthogonality#Euclidean_vector_spaces

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