On an integral representation of the normalized trace of the $k$-th symmetric tensor power of matrices and some applications

Hassan Issa, Hassan Abbas, Bassam Mourad

Let $A$ be an $n\times n$ matrix and let ${\vee }^{k}A$ be its $k$-th symmetric tensor product. We express the normalized trace of ${\vee }^{k}A$ as an integral of the $k$-th powers of the…