 Rank-one connection

Two constant deformation gradients are rank-one connected when their difference is an outer product $a\otimes N$. For a nonzero jump its matrix rank is one; equality $A=B$ is the trivial compatible case. The vector $N$ specifies a reference interface normal, and $a$ is the jump amplitude. The Hadamard jump condition identifies this algebraic condition with continuity of an affine deformation across a planar interface. The normal can be normalized by rescaling $a$ without changing the product.