# Skew Symmetric

### Some articles on skew, skew symmetric:

Parallel Axes Rule - Moment of Inertia Matrix - Identities For A Skew-symmetric Matrix
... In order to compare 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 computed using the matrix formed by the outer product ...
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 gives the same vector as the product ... Skew symmetric matrices generate orthogonal matrices with determinant 1 through the exponential map ... 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 can be also calculated ...
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 ... Lie algebra consisting of complex skew-hermitian traceless 2 x 2 matrices, which is isomorphic to ... matrices and thus the geodesics through I are have the form exp Xt where X is a skew-symmetric matrix ...
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 satisfies ... A = (aij) then the skew symmetric condition is aij = −aji ... For example, the following matrix is skew-symmetric ...
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 ...