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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2018 Volume 472, Pages 31–43 (Mi znsl6638)

This article is cited in 4 papers

Permanent preserving linear transformations of skew-symmetric matrices

M. V. Budrevichab, A. E. Gutermanab, M. A. Duffnerc

a Lomonosov Moscow State University, Moscow, Russia
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region, Russia
c Universidade de Lisboa, Lisboa, Portugal

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.

UDC: 512.643

Received: 06.11.2018



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