orthogonal

Etymology

By surface analysis, ortho- + -gon + -al. From French orthogonal, from Medieval Latin orthogōnālis, from Latin orthogōnius (“right-angled”).

adj

1. (geometry) Of two objects, at right angles; perpendicular to each other.
   A chord and the radius that bisects it are orthogonal.
2. (mathematics)
   1. Of a pair of vectors: having a zero inner product; perpendicular.
      The normal vector and tangent vector at a given point are orthogonal.
   2. Of a square matrix: such that its transpose is equal to its inverse.
   3. Of a linear transformation: preserving its angles.
   4. Of grid graphs, board games and polyominoes: vertical or horizontal but not diagonal.
   5. Of a pair of elements in an ortholattice: each less than or equal to the orthocomplement of the other.
3. (statistics) Statistically independent, with reference to variates.
4. (software engineering) Of two or more aspects of a problem, able to be treated separately; of a design, exhibiting consistency and composability.
   The content of the message should be orthogonal to the means of its delivery.
   An orthogonal approach also promotes reuse. If components have specific, well-defined responsibilities, they can be combined with new components in ways that were not envisioned by their original implementors. 1999, Andrew Hunt, David Thomas, The Pragmatic Programmer: From Journeyman to Master, Addison-Wesley Professional, page 36
5. Of two or more problems or subjects, independent of or irrelevant to each other.

noun

1. An orthogonal line