Pairs of matrices that have the same immanant

Maria Do Rosário Fernandes

doi:10.1080/03081089608818436

Pairs of matrices that have the same immanant

Maria Do Rosário Fernandes

DM - Departamento de Matemática

Research output: Contribution to journal › Article › peer-review

Abstract

Let χ be an irreducible C-character on the symmetric group S_n and B = [b_ij] be an n × n matrix over C. The function d_χ(B) = ∑_σ∈Sn χ(σ) Π_i=1ⁿ b_iσ(i) called an immanant. The main result of this paper is describing some matrices A satisfying d_χ(AB) = d_χ(B) for a given matrix B.

Original language	English
Pages (from-to)	193-201
Number of pages	9
Journal	Linear and Multilinear Algebra
Volume	40
Issue number	3
DOIs	https://doi.org/10.1080/03081089608818436
Publication status	Published - 1 Jan 1996

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title = "Pairs of matrices that have the same immanant",

abstract = "Let χ be an irreducible C-character on the symmetric group Sn and B = [bij] be an n × n matrix over C. The function dχ(B) = ∑σ∈Sn χ(σ) Πi=1n biσ(i) called an immanant. The main result of this paper is describing some matrices A satisfying dχ(AB) = dχ(B) for a given matrix B.",

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N2 - Let χ be an irreducible C-character on the symmetric group Sn and B = [bij] be an n × n matrix over C. The function dχ(B) = ∑σ∈Sn χ(σ) Πi=1n biσ(i) called an immanant. The main result of this paper is describing some matrices A satisfying dχ(AB) = dχ(B) for a given matrix B.

AB - Let χ be an irreducible C-character on the symmetric group Sn and B = [bij] be an n × n matrix over C. The function dχ(B) = ∑σ∈Sn χ(σ) Πi=1n biσ(i) called an immanant. The main result of this paper is describing some matrices A satisfying dχ(AB) = dχ(B) for a given matrix B.

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Pairs of matrices that have the same immanant

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