$E$ is a real, positive-definitive 3x3 symmetric tensor (I am thinking about the strain tensor in solid mechanics). We perform eigendecomposition and get:
$$E_p=\sum_{i=1}^{3}λ_iN_i⊗N_i$$
into its principal components, where $λ_i$ are its eigenvalues and $N_i$ are its eigenvectors. My question is, is there a closed form solution for $\frac{∂λ_i}{∂E}$ ?