Calculating d33 coefficient from Piezoelectric Tensor (eᵢⱼ) and Compliance Tensor (Sᵢⱼ)

Dear all,

I know this is a very basic question to ask. But, I couldn’t find a suitable reference to understand. It will be really helpful if someone helps me to understand these and/or provide some references to follow.

From the MP documentation-
dᵢⱼₖ[T] = eᵢₗₘSₗₘⱼₖ[E,T]

1) Now, eᵢⱼ is a [3x6] matrix and Sᵢⱼ is a [6x6] matrix. How can I multiply to get dᵢⱼ?
From the above article, I can understand how they are reducing the suffix numbers [11↦1, 22↦2, 33↦3, 23, 32↦4, 13, 21↦5, 12, 21↦6]

2) But, I can’t understand the relationship between this with i, j, k, l and m.

Kind regards,