First, define what you imagine a local element matrix is. For example, to get the same effect as switching reference coordinate system to parent, checking Use Selection Center and selecting the element to manipulate it, you only need the center of the element and move the identity matrix there as the TriMesh manipulation already works in the local coordinates (it's quite different if you want to transform the elements using their center like this). For other use cases, tell us first what effect you want to achieve.
Then it's simple, a quick example would be:
