An invariant ensemble is a random matrix that is unchanged under an adjoint action of a group of invariance. In this talk we will focus on sums/products of such ensembles, where general formulae for those eigenvalue probability density functions are provided, connecting eigenvalue PDFs to additive/multiplicative weights. There, a matrix addition/multiplication corresponds to convolution of their weights. Such connections can be shown for the additive spaces of the Hermitian, Hermitian antisymmetric, Hermitian anti-self-dual, and complex rectangular matrices as well as for the two multiplicative matrix spaces of the positive definite Hermitian matrices and of the unitary matrices. This is a joint work with Mario Kieburg (arXiv:2007.15259 [math-ph]).