I. (ˈ)ȯ(r)|thägən ə l adjective
Etymology: Middle French, from Latin orthogonius orthogonal (from Greek orthogōnios, from orth- + -gōnios, from -gōnia angle) + Middle French -al — more at -gon
1. : lying or intersecting at right angles : rectangular , right-angled
wind and sea may displace the ship's center of gravity along three orthogonal axes — C.C.Shaw
in orthogonal cutting, the cutting edge is perpendicular to the direction of tool travel — M.E.Merchant & Hans Ernst
2.
a. : mutually perpendicular
two vector functions the integral of whose scalar product throughout space is zero are orthogonal
b. : completely independent
two statistical variables having zero correlation are orthogonal
mental ability may be classified into several orthogonal … factors — O.D.Duncan
• or·thog·o·nal·ly -gən ə lē, -gnəlē adverb
II. noun
( -s )
: an imaginary line at right angles to wave crests in oceanography
III. adjective
1. : having a sum of products or an integral that is zero or sometimes 1 under specified conditions: as
a. of real-valued functions : having the integral of the product of each pair of functions over a specific interval equal to zero
b. of vectors : having the scalar product equal to zero
c. of a square matrix : having the sum of products of corresponding elements in any two rows or any two columns equal to 1 if the rows or columns are the same and equal to zero otherwise : having a transpose with which the product equals the identity matrix
2. of a linear transformation : having a matrix that is orthogonal : preserving length and distance
3. : composed of mutually orthogonal elements
an orthogonal basis of a vector space