Antisymmetric

Antisymmetric

Linear Algebra

Published in Russell L. Herman, A Course in Mathematical Methods for Physicists, 2013

A symmetric matrix is one for which the transpose of the matrix is the same as the original matrix, AT = A. An antisymmetric matrix is one that satisfies AT = −A. Show that the diagonal elements of an n × n antisymmetric matrix are all zero.Show that a general 3 × 3 antisymmetric matrix has three independent off-diagonal elements.How many independent elements does a general 3 × 3 symmetric matrix have?How many independent elements does a general n × n symmetric matrix have?How many independent elements does a general n × n antisymmetric matrix have?

Set Theory for Concept Modeling

View Chapter

Purchase Book

Published in Richard M. Golden, Statistical Machine Learning, 2020

Richard M. Golden

For example, if S ≡ {1, 2, 3}, then R ≡ {(1, 2), (2, 3), (1, 1)} is an antisymmetric relation but the relation R ≡ {(1, 2), (2, 1), (2, 3), (1, 1)} is not an antisymmetric relation on {1, 2, 3}.

Minimal realisations of odd transfer functions for first-degree nD systems

View Article

Journal Information

Published in International Journal of Control, 2020

De-Yin Zheng

For the sake of subsequent calculations, we review some notions and results. A skew-symmetric (or antisymmetric or antimetric (Reyment & Jöreskog, 1996)) matrix is a square matrix whose transpose is its negation; that is, it satisfies the condition AT = −A. If the entry in the ith row and jth column is ai, j, i.e. A = (ai, j) then the skew-symmetric condition is ai, j = −aj, i. A skew-symmetric determinant of odd order vanishes. The even-dimensional case can be calculated by the Pfaffian function of the matrix. These are the following two lemmas.

Explore chapters and articles related to this topic

Linear Algebra

Set Theory for Concept Modeling

Minimal realisations of odd transfer functions for first-degree nD systems