Abstract:
Let $Q_n(\mathbb{C})$ denote the space of all skew-symmetric $n\times n$ matrices over the complex field $\mathbb{C}$. The paper characterizes the linear mappings $T$: $Q_n(\mathbb{C})\to Q_n(\mathbb{C})$ that satisfy the condition $\operatorname{per}( T (A))=\operatorname{per}(A)$ for all $A \in Q_n(\mathbb{C})$ and an arbitrary $n>4$.
Key words and phrases:determinant, permanent, immanant, linear maps, skew-symmetric matrices.