Antisymmetric
Definition
Possessing the property of antisymmetry; changing its algebraic sign upon the inversion of elements (in mathematics and physics) or involving a binary relation where if one element relates to a second and vice versa, then the two elements are necessarily identical (in logic and set theory). In linear algebra, the term describes square matrices whose transpose equals their negative.
Bilingual Equivalents
- Antisymmetric
- Skew-symmetric
Grammatical & Source Details
| Inflection Type | Variable adjective with standard masculine, feminine, and structural plural variations. |
| Formation | Derived through prefixation, combining the prefix 'anti-' with the descriptive scientific adjective 'simetric' (symmetric). |
| Spelling / Pronunciation | [an.ti.si.ˈme.trik] |
| Source | Glossary of Linear Algebra, Set Theory, Logic, and Quantum Mechanics |
Contextual Usage Examples
RO: Profesorul a demonstrat la tablă că diagonala principală a unei matrici cu caracter antisimetric este compusă exclusiv din zerouri.
EN: The professor demonstrated on the board that the main diagonal of a skew-symmetric matrix is composed exclusively of zeros.
RO: Relația de ordine parțială pe o mulțime este definită structural ca fiind reflexivă, tranzitivă și complet antisimetrică.
EN: The partial order relation on a set is structurally defined as being reflexive, transitive, and completely antisymmetric.
RO: În fizica cuantică, funcția de undă a unui sistem format din fermioni identici trebuie să fie obligatoriu antisimetrică la schimbarea particulelor.
EN: In quantum physics, the wave function of a system composed of identical fermions must strictly be antisymmetric upon particle exchange.
Idioms & Phrases
Matrice antisimetrică / Skew-symmetric matrix
RO: Matrice pătratică egală cu opusa transpusei sale, având toate elementele de pe diagonala principală egale cu zero.
EN: A square matrix that is equal to the negative of its transpose, having all elements on the main diagonal equal to zero.
Relație antisimetrică / Antisymmetric relation
RO: Proprietate a unei relații binare prin care coincidența reciprocă a două elemente implică identitatea lor absolută.
EN: A property of a binary relation whereby the mutual coincidence of two elements implies their absolute identity.
Tensor antisimetric / Antisymmetric tensor
RO: Obiect matematic multidimensional care își schimbă semnul valorii atunci când doi indici oarecare sunt inversați între ei.
EN: A multidimensional mathematical object that changes its sign value when any two indices are swapped with each other.
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