orthogonal to vs orthogonal with

Both 'orthogonal to' and 'orthogonal with' are correct, but they are used in slightly different contexts. 'Orthogonal to' is more commonly used when describing the relationship between two things that are perpendicular or independent of each other. 'Orthogonal with' can be used when discussing the relationship between two things that are related but distinct.

Last updated: March 29, 2024 • 654 views

orthogonal to

This phrase is correct and commonly used in English.

This phrase is used to describe the relationship between two things that are perpendicular or independent of each other.

Examples:

The two vectors are orthogonal to each other.
Her opinion is orthogonal to mine.

Show examples from the web [+]

The horizontal, longitudinal and lateral planes are orthogonal to each other (see Figure 1).
For trajectories including reflections onto vertical surfaces not orthogonal to the incident plane, another vertical plane is subsequently considered including the reflected part of the propagation path.
The load is to be applied through the centreline of the hinge pin in a direction orthogonal to the longitudinal and transverse loads. (see Figure 5-2).
For doors which open in a vertical direction, the tests are intended to also establish minimum performance requirements and a test procedure for evaluating the primary latch system in a direction orthogonal to the first two directions.
Orthogonal to this line?
The equivalent height of a point is its orthogonal height in relation to the mean ground plane.
source lines representing conveyor belts, pipe lines, etc., sound power per metre length LW' and directivity as a function of the two orthogonal coordinates to the axis of the source line,
Are within the projection of the frontal silhouette of the motorcycle on an orthogonal plane perpendicular to the longitudinal median plane of the vehicle.
The parametric engines are jammed. Orthogonal vector's gone.
'Illuminating surface of a lighting device' (points 1.5.7 to 1.5.10) means the orthogonal projection of the full aperture of the reflector in a transverse plane.
But it seems I was simply rotated into an orthogonal time that runs at right angles to this one.
Dynamorphic generators, conceptual geometer, beam synthesizer, orthogonal engine filters.
The following tests shall be carried out along each of the three orthogonal axes of the test item.
The three-dimensional reference system is defined by three orthogonal planes established by the vehicle manufacturer (see figure).
For a point source, sound power LW and directivity as a function of the three orthogonal coordinates (x, y, z);
The computer revolution, the technocratic, technological revolution, has allowed us to jettison normal-shaped buildings, traditionally shaped buildings, in favor of non-orthogonal buildings such as this.
The test item shall be sinusoidally vibrated for three hours along each of its orthogonal axes in accordance with:
Vibrate the component for 30 minutes, pressurised, and sealed at the downstream side along each of the three orthogonal axes at the most severe resonant frequency determined as follows:
'Exterior light-emitting surfaces', for a defined direction of observation, means the orthogonal projection of the surface of light emission in a plane perpendicular to the direction of observation (see drawing in Appendix 1).
What would economies look like if we took that vision of human nature at their heart and stretched them along these orthogonal dimensions of the human psyche?

Alternatives:

perpendicular to
independent of
unrelated to
at right angles to
mutually exclusive with

orthogonal with

This phrase is correct but less commonly used than 'orthogonal to'. It can be used when discussing the relationship between two things that are related but distinct.

This phrase can be used to describe the relationship between two things that are related but distinct.