Definitions For Antisymmetric

Adjective

(not comparable) (set theory, order theory, of a binary relation R on a set S) Having the property that, for any two distinct elements of S, at least one is not related to the other via R; equivalently, having the property that, for any x, y ∈ S, if both xRy and yRx then x=y. (linear algebra, of certain mathematical objects) Whose sign changes on the application of a matrix transpose or some generalisation thereof: (of a matrix) Whose transpose equals its negative (i.e., MT = −M); {{quote-book, en, year=1974, author=Robert McCredie May, title=Stability and Complexity in Model Ecosystems, pageurl=https://books.google.com.au/books?id=BDA5-ipCLt4C&pg=PA193&dq=%22antisymmetric+matrix%22&hl=en&sa=X&ved=0ahUKEwjozKHrmN3bAhXROn0KHR-XBbwQ6AEIJzAA#v=onepage&q=%22antisymmetric%20matrix%22&f=false, page=193, publisher=w:Princeton University Press (of a tensor) That changes sign when any two index, indices are interchanged (e.g., Tijk = -Tjik); {{quote-book, en, year=1986, author=Millard F. Beatty Jr., title=Principles of Engineering Mechanics, Volume 1: Kinematics - The Geometry of Motion, publisher=Plenum Press, pageurl=https://books.google.com.au/books?id=q6lmnT1M86YC&pg=PA163&dq=%22antisymmetric%22&hl=en&sa=X&ved=0ahUKEwibup-ku9zbAhVlMn0KHYaGAXsQ6AEIPjAE#v=onepage&q=%22antisymmetric%22&f=false, page=163 (of a bilinear form) For which B(w,v) = -B(v,w). {{quote-book, en, year=2012, author=Stephanie Frank Singer, title=Symmetry in Mechanics: A Gentle, Modern Introduction, pageurl=https://books.google.com.au/books?id=D1blBwAAQBAJ&pg=PA28&dq=%22antisymmetric+bilinear%22&hl=en&sa=X&ved=0ahUKEwiMg-Dh_tzbAhWCD5AKHY0qBUUQ6AEIOjAD#v=onepage&q=%22antisymmetric%20bilinear%22&f=false, page=28, publisher=Springer

Synonyms

linear algebra skew-symmetric

Derived terms

antisymmetricity

Related terms

antisymmetry symmetric

Translations

Czech: antisymetrický Finnish: antisymmetrinen French: antisymétrique German: antisymmetrisch Icelandic: andsamhverfur, m Japanese: 反対称的 (はんたいしょうてき, han-taishō-teki, sc=Jpan) Polish: antysymetryczny Portuguese: antissimétrico Romanian: antisimetric Russian: антисимметричный, sc=Cyrl Spanish: antisimétrico Swedish: antisymmetrisk Finnish: antisymmetrinen German: antisymmetrisch Polish: antysymetryczny Romanian: antisimetric Spanish: antisimétrico