Skew-Symmetric Matrices and the Hat Operator

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In this section, we'll talk about properties of skew-symmetric matrices and the hat operator.

Skew-Symmetric Matrices

A skew-symmetric matrix must have all 0 on its diagonal.

In particular, notice that because of the constraints for skew symmetry, this matrix only has three independent parameters.

The hat operator can switch beetween skew-sysmmetric matrix and a column vector.

Hat Operator

The cross product can be expressed by hat operator.

Example: Representation of Angular Velocities

Ref: Skew-Symmetric Matrices and the Hat Operator

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