adjective

- Mathematics.
- Also orthographic.pertaining to or involving right angles or perpendiculars: an orthogonal projection.
- (of a system of real functions) defined so that the integral of the product of any two different functions is zero.
- (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.
- (of two vectors) having an inner product equal to zero.
- (of a linear transformation) defined so that the length of a vector under the transformation equals the length of the original vector.
- (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.

adjective

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

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