orthogonalize
C2Formal, Technical, Academic
Definition
Meaning
To make orthogonal, i.e., to transform or arrange vectors or data points so that they are perpendicular or statistically independent.
In a figurative sense, to make two concepts, arguments, or processes unrelated, independent, or non-overlapping, so that they can be considered separately.
Linguistics
Semantic Notes
Primarily a mathematical/computational verb. Rarely used in general discourse. The noun 'orthogonalization' is more common than the verb in certain fields.
Dialectal Variation
British vs American Usage
Differences
No significant difference in meaning or usage. Spelling difference follows general -ise/-ize convention: 'orthogonalise' is a UK variant, though -ize is also common and accepted in UK technical contexts.
Connotations
Identical highly technical connotations in both varieties.
Frequency
Extremely low frequency in both, but slightly higher in US technical writing due to a stronger STEM publishing sector.
Vocabulary
Collocations
Grammar
Valency Patterns
[Verb] + [direct object: set/vectors/data]It + [is/was] + [adjective: necessary/crucial] + [to-infinitive: to orthogonalize] + [object].Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “orthogonalize the problem (figurative, in problem-solving)”
Usage
Context Usage
Business
Almost never used. Possibly in highly technical finance or data analysis to mean 'remove correlation'.
Academic
Common in mathematics, linear algebra, signal processing, quantum mechanics, and statistics papers.
Everyday
Virtually never used.
Technical
The primary domain of use. Refers to algorithms (e.g., Gram-Schmidt process) and data preprocessing.
Examples
By Part of Speech
verb
British English
- The first step is to orthogonalise the basis vectors using the Gram-Schmidt process.
- We must orthogonalise the components to ensure statistical independence.
American English
- The algorithm is designed to orthogonalize the input signals, reducing interference.
- To solve the system efficiently, we need to orthogonalize the columns of the matrix.
adverb
British English
- N/A (adverb is 'orthogonally')
American English
- N/A (adverb is 'orthogonally')
adjective
British English
- N/A (adjective is 'orthogonal')
American English
- N/A (adjective is 'orthogonal')
Examples
By CEFR Level
- Advanced data analysis often requires you to orthogonalize variables to avoid multicollinearity.
- The researcher explained the need to orthogonalize the different factors influencing the outcome.
Learning
Memory Aids
Mnemonic
Think of an ORTHOdontist (teeth doctor) making teeth straight and at right angles. 'Orthogonalize' makes data 'straight' and at right angles to each other.
Conceptual Metaphor
INDEPENDENCE IS PERPENDICULARITY; PURIFICATION IS REMOVING OVERLAP.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid direct translation to 'ортогонализировать' unless in a strict mathematical context; the Russian term is equally technical. In figurative use, 'to make independent/unrelated' is better.
Common Mistakes
- Using it in non-technical conversation; Confusing with 'normalize' or 'standardize'; Incorrectly forming the noun as 'orthogonalization'.
Practice
Quiz
In which field is the verb 'to orthogonalize' most commonly used?
FAQ
Frequently Asked Questions
Yes, it is a standard, though highly technical, verb in mathematics, engineering, and data science.
'Normalize' typically means to scale to a standard range (often 0 to 1 or a unit length). 'Orthogonalize' means to make perpendicular or statistically independent, which often involves changing direction, not just scale.
It would sound very unusual and pretentious. In everyday contexts, use phrases like 'make unrelated', 'separate', or 'untangle' instead.
The Gram-Schmidt process is the classic algorithm for orthogonalizing a set of vectors in an inner product space.