変形
F e 2 = F 12 e 1 + F 22 e 2 = γ e 1 + e 2 ⟹ F ( e 2 ⊗ e 2 ) = γ e 1 ⊗ e 2 + e 2 ⊗ e 2 {\displaystyle F{\boldsymbol {e}}_{2}=F_{12}{\boldsymbol {e}}_{1}+F_{22}{\boldsymbol {e}}_{2}=\gamma {\boldsymbol {e}}_{1}+{\boldsymbol {e}}_{2}\quad \implies \quad F({\boldsymbol {e}}_{2}\otimes {\boldsymbol {e}}_{2})=\gamma {\boldsymbol {e}}_{1}\otimes {\boldsymbol {e}}_{2}+{\boldsymbol {e}}_{2}\otimes {\boldsymbol {e}}_{2}}
e i ⊗ e i = 1 {\displaystyle {\boldsymbol {e}}_{i}\otimes {\boldsymbol {e}}_{i}={\boldsymbol {\mathit {1}}}} であるため、変形勾配を以下のように記述することもできる。
F = 1 + γ e 1 ⊗ e 2 {\displaystyle F={\boldsymbol {\mathit {1}}}+\gamma {\boldsymbol {e}}_{1}\otimes {\boldsymbol {e}}_{2}}