Geodesic
Permanent preserving linear transformations of skew-symmetric matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXI, Tome 472 (2018), pp. 31-43

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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 $n>4$. 
@article{ZNSL_2018_472_a2,
     author = {M. V. Budrevich and A. E. Guterman and M. A. Duffner},
     title = {Permanent preserving linear transformations of skew-symmetric matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {31--43},
     publisher = {mathdoc},
     volume = {472},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_472_a2/}
}
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M. V. Budrevich; A. E. Guterman; M. A. Duffner. Permanent preserving linear transformations of skew-symmetric matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXI, Tome 472 (2018), pp. 31-43. http://geodesic.mathdoc.fr/item/ZNSL_2018_472_a2/