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