# Skew Symmetric

### Some articles on skew, skew symmetric:

Skew-symmetric Matrix
... In mathematics, and in particular linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix A whose transpose is also its negative that is, it ... A = (aij) then the skew symmetric condition is aij = −aji ... For example, the following matrix is skew-symmetric ...
Riemannian Connection On A Surface - Example: The 2-sphere
... The Lie algebra of SO(3) consists of all skew-symmetric real 3 x 3 matrices ... geodesics through I are have the form exp Xt where X is a skew-symmetric matrix ... equation") of the form gt = A · g where A(t) is skew-symmetric and g takes values in SO(3) ...
Charts On SO(3) - Parametrizations - Problems of The Parametrizations
... If we use a skew-symmetric matrix, every 3×3 skew-symmetric matrix is determined by 3 parameters, and so at first glance, the parameter space is R3 ... A similar situation holds for applying a Cayley transform to the skew-symmetric matrix ...
Parallel Axes Rule - Moment of Inertia Matrix - Identities For A Skew-symmetric Matrix
... formulations of the parallel axis theorem using skew-symmetric matrices and the tensor formulation, the following identities are useful ... Let be the skew symmetric matrix associated with the position vector R=(x, y, z), then the product in the inertia matrix becomes This product can be ...
Bivector - Three Dimensions - Matrices
... Bivectors are isomorphic to skew-symmetric matrices the general bivector B23e23 + B31e31 + B12e12 maps to the matrix This multiplied by vectors on both sides ... Skew symmetric matrices generate orthogonal matrices with determinant 1 through the exponential map ... a rotation matrix, that is the rotation matrix MR given by the above skew-symmetric matrix is The rotation described by MR is the same as that described by the rotor R given by and the matrix MR ...