An immanant, associated to an irreducible complex character \(\chi\) of symmetric group \(S_n\), is a function \(d_\chi:M_n({\mathbb F})\to {\mathbb F}\), defined by \[ d_\chi(A):=\sum_{\sigma\in S_n}\chi(\sigma)\prod^n_{i=1}a_{i\sigma(i)} \qquad\forall A=(a_{ij})\in M_n({\mathbb F}). \] This includes the determinant (when \(\chi\) is alternating character) and the permanent (when \(\chi\) is constantly \(1\)). The authors study surjective mappings \(T:M_n({\mathbb C})\to M_n(\mathbb C)\), on \(n\)-by-\(n\) complex matrices, which transform one immanant into another. Linearity is not assumed; its rudiments are only weakly embedded into the functional equation via \[ d_{\chi}(T(A)+\alpha T(B))=d_{\lambda}(A+\alpha B)\qquad\forall\alpha \in {\mathbb C},\;\forall A,B\in M_n({\mathbb C}).\tag{1} \] It is shown that such a surjection must automatically be linear. This is a nice generalization of the previously obtained results on determinants, due to \textit{G. Dolinar} and \textit{P. Šemrl} [ibid. 348, No. 1--3, 189--192 (2002; Zbl 0998.15011)], and extended by \textit{V. Tan} and \textit{F. Wang} [ibid. 369, 311--317 (2003; Zbl 1032.15004)]. As a consequence, it follows by earlier work of the authors that no surjection \(T\) can satisfy (1) if characters \(\chi\) and \(\lambda\) differ, except when \(\chi,\lambda\) are characters of \(S_4\) that correspond to partitions \([2,1,1]\) and \([3,1]\), respectively. When \(\chi=\lambda\), the general form of linear surjections that satisfy (1) are also known. The relevant papers are pointed out in the references. The main idea of the proof is (i) a classification of the set \({\mathcal A}_{\chi}\) of all matrices \(A\) with the property that the polynomial \(p(\alpha):=d_\chi(A+\alpha B)\) has degree at most one for any \(B\) and (ii) when \(\chi\) is not an alternating character, a classification of all subspaces of dimension \(n\) contained in \({\mathcal A}_\chi\).