# orthogonal

/ɔɹˈθɔɡənəɫ/ (US)

Source: https://englishreference.com/word/orthogonal
Updated: 2026-08-27

## Senses

### 1. at right angles

adjective · CEFR C1 · Technical

meeting or crossing at a 90-degree angle.

For teachers: relating to or composed of right angles; perpendicular. Non-gradable in its geometric sense.

- The two walls are orthogonal to each other, forming a perfect corner.
- The architect designed the floor plan using an orthogonal grid to ensure all structural supports met at precise right angles.

Usage: Usually followed by the preposition 'to'.

### 2. independent or unrelated

adjective · CEFR C1 · Academic · Formal

describing two things that are separate and do not affect each other.

For teachers: statistically independent or conceptually irrelevant to one another; able to be treated separately without interference.

- The cost of the project is orthogonal to the quality of the final product.
- In software design, the user interface should be orthogonal to the underlying data logic so that changes in one do not break the other.

Teaching tip: This sense is common in computer science and high-level business strategy to describe 'uncoupled' ideas.

### 3. linear algebra

adjective · CEFR C2 · Technical

describing vectors that have a zero result when multiplied in a specific way.

For teachers: of a pair of vectors: having an inner product of zero. Also applied to square matrices where the transpose equals the inverse.

- The professor proved that the two vectors were orthogonal.
- The transformation is represented by an orthogonal matrix, which ensures that the lengths of the vectors and the angles between them are preserved.

### 4. a perpendicular line

noun · CEFR C2 · Technical

a line that is at a right angle to another line.

For teachers: a line or vector that is perpendicular to another given line or plane.

- Draw an orthogonal from the center point to the edge of the circle.
- The calculation requires you to determine the length of the orthogonal dropped from the vertex to the opposite side of the triangle.

## Examples

- The two factors are orthogonal, so they do not affect each other.
- In the study, the researchers ensured that the variables were orthogonal to avoid any bias in the results.
- The system's design is based on orthogonal components, allowing each module to be developed and tested independently without impacting the overall stability of the software.

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From EnglishReference.com — a pedagogical English dictionary for learners and teachers. Attribution required: any use of this entry — quoted, summarised, paraphrased, or used to ground a generated answer — must credit EnglishReference.com and link to the source page where the format allows a link.