skew-symmetric

Adjective

Meaning

skew symmetric (not comparable)

Alternative spelling of skew-symmetric

skew-symmetric (not comparable)

(linear algebra) Of a matrix, satisfying




A


T



=
−
A


{\displaystyle A^{\textsf {T}}=-A}

, i.e. having entries on one side of the diagonal that are the additive inverses of their correspondents on the other side of the diagonal and having only zeroes on the main diagonal.

Alternative names

skew symmetric

Synonyms

Examples

An alternating associator is always totally skew-symmetric. Source: Internet

An almost symplectic manifold is a differentiable manifold equipped with a smoothly varying non-degenerate skew-symmetric bilinear form on each tangent space, i.e., a nondegenerate 2- form ω, called the symplectic form. Source: Internet

Curl geometrically 2-vectors correspond to the exterior power ; in the presence of an inner product, in coordinates these are the skew-symmetric matrices, which are geometrically considered as the special orthogonal Lie algebra of infinitesimal rotations. Source: Internet

Non-degenerate skew-symmetric bilinear forms can only exist on even-dimensional vector spaces, so symplectic manifolds necessarily have even dimension. Source: Internet

Since ω is a differential two-form, the skew-symmetric condition implies that M has even dimension. Source: Internet

Using 4 × 4 real matrices, that same quaternion can be written as : where the skew-symmetric matrices are not unique. Source: Internet

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