skew symmetry: meaning, definition, pronunciation and examples
C2 (Proficiency)Highly technical/academic; primarily used in mathematics, physics, and theoretical disciplines.
Quick answer
What does “skew symmetry” mean?
A property of a mathematical object, matrix, or function that is equal to the negative of its transpose or reflection.
Audio
Pronunciation
Definition
Meaning and Definition
A property of a mathematical object, matrix, or function that is equal to the negative of its transpose or reflection; asymmetry with a specific mathematical relationship where f(x,y) = -f(y,x).
A term describing any system, relationship, or arrangement that exhibits a balanced but opposite asymmetry, often used metaphorically in fields like art, sociology, or biology to describe patterns where two sides are mirror opposites in a specific, anti-symmetric way.
Dialectal Variation
British vs American Usage
Differences
No significant difference in technical meaning. 'Skew-symmetric' (with hyphen) is slightly more common in British academic writing, while 'skew symmetric' (without hyphen) is equally accepted in American texts.
Connotations
Identical technical connotations. Both varieties understand it as a formal, precise mathematical term.
Frequency
Extremely low frequency in general language. Usage is almost exclusively confined to advanced STEM publications and lectures in both varieties.
Grammar
How to Use “skew symmetry” in a Sentence
The matrix [subject] exhibits skew symmetry.Skew symmetry is a property of [noun phrase].[Noun] is skew-symmetric.One can prove the skew symmetry of [object].Vocabulary
Collocations
Examples
Examples of “skew symmetry” in a Sentence
verb
British English
- The operator does not skew-symmetrise under that transformation.
- To solve the equation, one must first skew the symmetry appropriately.
American English
- The transformation skew-symmetrizes the tensor.
- We can skew the matrix to test for symmetry.
adverb
British English
- The forces were arranged skew-symmetrically about the pivot.
- The entries are distributed skew-symmetrically.
American English
- The matrix is configured skew symmetrically.
- The values vary skew symmetrically across the diagonal.
adjective
British English
- The cross product yields a skew-symmetric matrix.
- They studied the skew-symmetrical properties of the Lie bracket.
American English
- The electromagnetic field tensor is skew symmetric.
- He identified a skew-symmetric component in the data.
Usage
Meaning in Context
Business
Virtually never used. Might appear in highly quantitative finance modelling discussions.
Academic
Core term in linear algebra, differential geometry, physics (especially mechanics and electromagnetism), and Lie theory.
Everyday
Not used.
Technical
The primary domain. Used to describe matrices (A^T = -A), cross products, certain tensors, and the structure of Lie algebras.
Vocabulary
Synonyms of “skew symmetry”
Strong
Neutral
Weak
Vocabulary
Antonyms of “skew symmetry”
Watch out
Common Mistakes When Using “skew symmetry”
- Using 'skew symmetry' to mean simple asymmetry or lack of balance.
- Confusing a skew-symmetric matrix with a symmetric matrix (where A^T = A).
- Incorrectly applying the term to visual patterns without the precise mathematical negative-transpose relationship.
FAQ
Frequently Asked Questions
No. The only matrix that is both symmetric and skew-symmetric is the zero matrix. They are opposite properties.
Yes. The concept applies to bilinear forms, tensors, functions (where f(x,y) = -f(y,x)), and the structure constants of Lie algebras.
Infinitesimal rotations in three-dimensional space are represented by skew-symmetric matrices. This links skew symmetry directly to angular motion.
It is fundamental in describing conservation laws (via Noether's theorem), electromagnetic fields (the field tensor is skew-symmetric), and the mathematics of rotational dynamics.
A property of a mathematical object, matrix, or function that is equal to the negative of its transpose or reflection.
Skew symmetry is usually highly technical/academic; primarily used in mathematics, physics, and theoretical disciplines. in register.
Skew symmetry: in British English it is pronounced /ˌskjuː ˈsɪm.ɪ.tri/, and in American English it is pronounced /ˌskjuː ˈsɪm.ə.tri/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think of 'skew' as slanted or off-center. In a skew-symmetric matrix, the diagonal is zero, and opposite entries are negatives of each other, like a balanced but opposite tilt across the diagonal.
Conceptual Metaphor
A HANDSHAKE THAT PUSHES AWAY: Imagine two people shaking hands, but instead of mutual grip, one person's push is perfectly countered by the other's equal and opposite push from the other side—a balanced opposition.
Practice
Quiz
What does skew symmetry imply for the diagonal entries of a real matrix?