Symbolic diagonalization, matrix differentiation and the wedge product
May I ask whether symbolic entry-wise differentiation of matrices can be done using SageMath? I would like to conduct the following operations:
1.Diagonalize a complicated symbolic matrix.
3.The wedge product. I need to be able to take the n-th power of a matrix of 1-forms.
4.Integration (I will take the trace first before integrations so integrations will not be done on matrices. The result is likely to be completely crazy but I assume this can be done)
Please let me know whether this is possible. Thank you very much!