Abstract
Let Σn(F) denote the space of all n×n symmetricmatrices over the complex field F, and χ be an irreducible character of Sn and dχ the immanant associated with χ. The main objective of this paper is to prove that the maps Φ: Σn(F) → Σn(F) satisfying dχ(Φ(A) + αΦ(B)) = det(A + αB) for all singular matrices A, B ∈ Σn(F) and all scalars α ∈ F are linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on the set of all symmetric matrices.
Original language | English |
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Pages (from-to) | 630-636 |
Number of pages | 7 |
Journal | Lobachevskii Journal of Mathematics |
Volume | 38 |
Issue number | 4 |
DOIs | |
State | Published - 1 Jul 2017 |
Externally published | Yes |
Keywords
- Determinant
- converters
- permanent
- symmetric matrices
All Science Journal Classification (ASJC) codes
- General Mathematics