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# Plucker matrix

Plucker matrices are a representation of a line used in relation to 3D homogeneous coordinates. Specifically, a Plucker matrix is a 4×4 skew-symmetric homogeneous matrix, defined as $mathbf\left\{P\right\} = AB^T - BA^T$, where $A$ and $B$ are two homogeneous coordinates on the line.

P has rank 2. Its 2 dimensional null-space is spanned by the pencil of planes with the line as axis. It has 4 degrees of freedom.