Generalized matrix functions and determinants

Jafari, Mohammad Hossein; Madadi, Ali Reza

doi:10.2478/s11533-013-0347-0

Cited by 3 publications

(2 citation statements)

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“…Proof. Since (AB) T = BA for every symmetric matrices A and B, (1) implies (2). Suppose that (2) is true.…”

Section: By Lemma 31(3)mentioning

confidence: 99%

“…By using such matrices along with the relation, a necessary and sufficient condition for the equality is proven (see Theorem 3.9). By applying S σ for some σ ∈ S n , we obtain Theorem 3.17 which related to Corollary 2.4. in [2]. By these results, to obtain the equalities on the set of all symmetric matrices, it suffices to work on the permutation group which is finite.…”

Section: Introductionmentioning

confidence: 99%

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The equality of generalized matrix functions on the set of all symmetric matrices

Sanguanwong

Rodtes

2019

Linear Algebra and its Applications

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A generalized matrix function d G χ : M n (C) → C is a function constructed by a subgroup G of S n and a complex valued function χ of G. The main purpose of this paper is to find a necessary and sufficient condition for the equality of two generalized matrix functions on the set of all symmetric matrices, S n (C). In order to fulfill the purpose, a symmetric matrix S σ is constructed and d G χ (S σ ) is evaluated for each σ ∈ S n . By applying the value of d G χ (S σ ), it is shown that d G χ (AB) = d G χ (A)d G χ (B) for each A, B ∈ S n (C) if and only if d G χ = det. Furthermore, a criterion when d G χ (AB) = d G χ (BA) for every A, B ∈ S n (C), is established.

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“…Proof. Since (AB) T = BA for every symmetric matrices A and B, (1) implies (2). Suppose that (2) is true.…”

Section: By Lemma 31(3)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The equality of generalized matrix functions on the set of all symmetric matrices

Sanguanwong

Rodtes

2019

Linear Algebra and its Applications

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Generalized matrix functions, permutation matrices and symmetric matrices

Jafari,

Madadi

2023

Filomat

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The purpose of this paper is to study generalized matrix functions only using the permutation matrices and symmetric matrices. Firstly the zeroness of a generalized matrix function and then the equality of two generalized matrix functions on the permutation matrices and symmetric matrices will be examined. Secondly generalized matrix functions preserving commutativity of the permutation matrices or commutativity of the symmetric matrices will be characterized. Thirdly generalized matrix functions which preserve product of the permutation matrices or product of the symmetric matrices will be investigated. Finally the Cayley-Hamilton Theorem for generalized characteristic polynomials using the permutation matrices and symmetric matrices will be studied.

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