# Immanant Conversion on Symmetric Matrices

M. Purificação Coelho; M. Antónia Duffner; Alexander E. Guterman

Special Matrices (2014)

- Volume: 2, Issue: 1, page 1-10, electronic only
- ISSN: 2300-7451

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topM. Purificação Coelho, M. Antónia Duffner, and Alexander E. Guterman. "Immanant Conversion on Symmetric Matrices." Special Matrices 2.1 (2014): 1-10, electronic only. <http://eudml.org/doc/267527>.

@article{M2014,

abstract = {Letr Σn(C) denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C) -> Σn (C) satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB) = dχ·(Φ(Α ) + αΦ(Β)) for all matrices A,В ε Σ„(С) and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С).},

author = {M. Purificação Coelho, M. Antónia Duffner, Alexander E. Guterman},

journal = {Special Matrices},

keywords = {Determinant; permanent; immanant; preservers; converters; symmetric matrices; determinant},

language = {eng},

number = {1},

pages = {1-10, electronic only},

title = {Immanant Conversion on Symmetric Matrices},

url = {http://eudml.org/doc/267527},

volume = {2},

year = {2014},

}

TY - JOUR

AU - M. Purificação Coelho

AU - M. Antónia Duffner

AU - Alexander E. Guterman

TI - Immanant Conversion on Symmetric Matrices

JO - Special Matrices

PY - 2014

VL - 2

IS - 1

SP - 1

EP - 10, electronic only

AB - Letr Σn(C) denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C) -> Σn (C) satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB) = dχ·(Φ(Α ) + αΦ(Β)) for all matrices A,В ε Σ„(С) and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С).

LA - eng

KW - Determinant; permanent; immanant; preservers; converters; symmetric matrices; determinant

UR - http://eudml.org/doc/267527

ER -

## References

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- [8] G.D. James, A. Kerber: The representation theory of the symmetric group, Encyclopedia of Mathematics and its Applications 16, Cambridge University Press, 1981.
- [9] B. Kuzma: A note on immanant preservers, Fundamental and Applied Mathematics, 13, 4, (2007) 113-120, translated in Journal of Mathematical Sciences (New York) 155:6 (2008), 872-876.
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