orthogonal

[ awr-thog-uh-nl ]

adjective

1. Mathematics.
   1. Also 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.
3. having no bearing on the matter at hand; independent of or irrelevant to another thing or each other:

   It’s an interesting question, but orthogonal to our exploration of the right to privacy.

orthogonal

/ ɔːˈθɒɡənəl /

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

orthogonal

/ ôr-thŏg′ə-nəl /

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.

Derived Forms

• orˈthogonally, adverb

Other Words From

• or·thog·o·nal·i·ty [awr-thog-, uh, -, nal, -i-tee], noun
• or·thog·o·nal·ly adverb

Word History and Origins

Origin of orthogonal¹

First recorded in 1565–75; obsolete orthogon(ium) “right triangle,” from Late Latin orthogōnium or directly from Greek orthogṓnion (neuter) “right-angled,” equivalent to ortho- ortho- + -gōnion -gon ) + -al ¹

Example Sentences

"Therefore, scattering correction is only performed along one dimension for a 2D image. To correct scattering in both dimensions, we need to scan the sample and correct scattering along the other dimension as well, resulting in an orthogonal scanning strategy."

From Science Daily

The combination of mutually orthogonal binding pair systems allowed a more precise identification and analysis of the mediator proteins that freely translocate between the ER and mitochondria, facilitating a deeper exploration of the proteins involved in the organelle contact sites and uncovering their roles in cellular functions and disease mechanisms.

From Science Daily

The "treadmill" also employed two high-speed orthogonal cameras to capture unique locomotion features -- one a side view, the other from the bottom.

From Science Daily

"Such modular implementation of this cycle in E. coli paves the way to the realization of highly complex, orthogonal new-to-nature CO2-fixation pathways in cell factories. We are learning to completely reprogram the cellular metabolism to create a synthetic autotrophic operating system for the cell."

From Science Daily

The technical term for each cherry red form is an orthotope, defined as “the Cartesian product of orthogonal intervals known as a hyperrectangle, sometimes called a parallelotope.”

From Los Angeles Times

Related Words

• rectangular