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

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.

Other Word Forms

• orthogonality noun
• orthogonally 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

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

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Their core provisions were always unlikely to substantially affect turnout or election outcomes — and they were also mostly orthogonal to the weak spots in the electoral system that Trump’s knavery attempted to exploit.

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“It is these areas where the flow will be orthogonal to the terrain and the greatest rainfall totals realized,” the Weather Prediction Center said.

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It encompasses an orthogonal attack on its targets — not merely the contraceptive mandate, but the ACA’s other mandates.

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Lines accreted in an essentially radial configuration, with large arcs orbiting an absent central axis, and orthogonal spokes sprouting from the core.

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Related Words

• rectangular 

When To Use

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.