# orthogonal

[ awr-thog-uh-nl ]
/ ɔrˈθɒg ə nl /

Mathematics.
1. Also orthographic. pertaining to or involving right angles or perpendiculars: an orthogonal projection.
2. (of a system of real functions) defined so that the integral of the product of any two different functions is zero.
3. (of a system of complex functions) defined so that the integral of the product of a function times the complex conjugate of any other function equals zero.
4. (of two vectors) having an inner product equal to zero.
5. (of a linear transformation) defined so that the length of a vector under the transformation equals the length of the original vector.
6. (of a square matrix) defined so that its product with its transpose results in the identity matrix.
Crystallography. referable to a rectangular set of axes.

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## Origin of orthogonal

1565–75; obsolete orthogon(ium) right triangle (<Late Latin orthogōnium<Greek orthogṓnion (neuter) right-angled, equivalent to ortho-ortho- + -gōnion-gon) + -al1

## OTHER WORDS FROM orthogonal

Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2020

## British Dictionary definitions for orthogonal

orthogonal
/ (ɔːˈθɒɡənəl) /

relating to, consisting of, or involving right angles; perpendicular
maths
1. (of a pair of vectors) having a defined scalar product equal to zero
2. (of a pair of functions) having a defined product equal to zero