Let \(C\) and \(\overline C\) denote two symmetric positive definite constant matrices. It follows from linear algebra that there are matrices \(F\) and \(\overline F\) such that: (*) \(F^ T F=C\), \(\text{det} F>0\); \(\overline{F}^ T\overline{F}=\overline C\), \(\text{det} \overline F>0\). If there are two vectors \(A\) and \(N\) such that (**) \(\overline F =F(I+A\otimes N)\), then \(F\) and \(\overline F\) can be interpreted as constant deformation gradients relative to a homogeneous reference configuration, and (**) represents a ``kinematic condition of compatibility'', permitting us to construct a continuous deformation with the deformation gradient jumping across a plane with normal \(N\). The author claims that such types of deformation occur in a theory of phase transitions in crystals, and he provides a number of conditions under which the matrices \(C\) and \(\overline C\) related by some rotation \(R\) through: \(\overline C=R^ T CR\), are compatible with equation (**).