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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