orthogonal

adjective

1. 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.
2. Crystallography. referable to a rectangular set of axes.

adjective

1. relating to, consisting of, or involving right angles; perpendicular
2. 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

adj.1570s, from French orthogonal, from orthogone, from Late Latin orthogonius, from Greek orthogonios “right-angled,” from ortho- “straight” (see ortho-) + gonia “angle,” related to gony “knee” (see knee (n.)). Related: Orthogonally.

1. Relating to or composed of right angles.
2. Relating to a matrix whose transpose equals its inverse.
3. Relating to a linear transformation that preserves the length of vectors.