orthogonal

American  

[awr-thog-uh-nl] / ɔrˈθɒg ə 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.

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orthogonal British  

/ 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

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orthogonal Scientific  

/ 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.

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Usage

What does orthogonal mean? Orthogonal means relating to or involving lines that are perpendicular or that form right angles, as in This design incorporates many orthogonal elements. Another word for this is orthographic. When lines are perpendicular, they intersect or meet to form a right angle. For example, the corners of squares and rectangles are all right angles. Orthogonal is a mathematical term that is also used in much more technical ways pertaining to vectors and functions. However, orthogonal is also sometimes used in a figurative way meaning unrelated, separate, in opposition, or irrelevant. In this sense, it means about the opposite of parallel when parallel means corresponding or similar. Example: Not everything happens according to a grand scheme—some events are simply orthogonal to each other.

Other Word Forms

• orthogonality noun
• orthogonally adverb

Etymology

Origin of orthogonal

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

Explanation

Two lines that are orthogonal are perpendicular or intersecting at a right angle, like a t-square used by draftsmen. The word orthogonal comes from the Greek orthogōnios meaning "right-angled." While this word is used to describe lines that meet at a right angle, it also describes events that are statistically independent, or do not affect one another in terms of outcome.

Example Sentences

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 • Feb. 20, 2024

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 • Aug. 12, 2022

If the planes are neither parallel nor orthogonal, then find the measure of the angle between the planes.

From Textbooks • Mar. 30, 2016

Projections allow us to identify two orthogonal vectors having a desired sum.

From Textbooks • Mar. 30, 2016

V. be perpendicular, be orthogonal; intersect at right angles, be rectangular, be at right angles to, intersect at 90 degrees; have no correlation.

From Roget's Thesaurus of English Words and Phrases by Roget, Peter Mark

Related Words

• rectangular