multilinear form: meaning, definition, pronunciation and examples
Very LowHighly Technical/Academic
Quick answer
What does “multilinear form” mean?
A function of several vector arguments that is linear in each argument separately.
Audio
Pronunciation
Definition
Meaning and Definition
A function of several vector arguments that is linear in each argument separately
A mathematical object defined on a Cartesian product of vector spaces that satisfies linearity properties with respect to each input variable when others are held fixed
Dialectal Variation
British vs American Usage
Differences
No differences in meaning; British texts might use 'alternating multilinear form' more frequently for determinant-like structures
Connotations
None beyond technical mathematical context
Frequency
Equally rare in both varieties, confined to advanced mathematics
Grammar
How to Use “multilinear form” in a Sentence
multilinear form on [vector space]multilinear form of degree [number]multilinear form in [number] variablesVocabulary
Collocations
Examples
Examples of “multilinear form” in a Sentence
verb
British English
- One can multilinearly extend this form to the whole space.
American English
- We multilinearly interpolate between the given values.
adverb
British English
- The map behaves multilinearly across all arguments.
American English
- The operator acts multilinearly on tensor products.
Usage
Meaning in Context
Business
Never used
Academic
Exclusively in advanced mathematics, physics, or engineering textbooks/research
Everyday
Never used
Technical
Core terminology in pure and applied mathematics, theoretical physics
Vocabulary
Synonyms of “multilinear form”
Strong
Neutral
Weak
Vocabulary
Antonyms of “multilinear form”
Watch out
Common Mistakes When Using “multilinear form”
- Using 'multilinear' to mean 'polynomial' or 'nonlinear'
- Confusing with 'multivariate function' (which isn't necessarily linear in each variable)
FAQ
Frequently Asked Questions
Yes, in most mathematical contexts they are synonymous, though 'form' sometimes implies scalar-valued outputs.
The area of a parallelogram computed via determinant (base × height) is essentially a multilinear form of two vectors.
A bilinear form has exactly two arguments; a multilinear form generalises this to any finite number of arguments.
Yes, in theoretical physics (relativity, quantum field theory) and some engineering fields (continuum mechanics).
Multilinear form is usually highly technical/academic in register.
Multilinear form: in British English it is pronounced /ˌmʌltiˈlɪnɪə fɔːm/, and in American English it is pronounced /ˌmʌltiˈlɪniər fɔːrm/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “The determinant is a classic example of an alternating multilinear form.”
Learning
Memory Aids
Mnemonic
MULTI + LINEAR = linear in many directions; like a multi-dimensional ruler measuring different inputs independently
Conceptual Metaphor
A machine with multiple input slots where changing one dial adjusts the output proportionally, regardless of other dial settings
Practice
Quiz
Where is 'multilinear form' primarily used?