On the number of matrices to generate a matrix ∗-algebra over the real field

In this paper, we discuss generating a ∗-algebra over the real field with a set of symmetric matrices. This is motivated by an application in structural engineering. We show that any ∗-algebra can be generated with at most four randomly-chosen symmetric matrices. The proof relies on the structure theorem for ∗-algebras and the notion of genericity in eigenvalue structure.