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On the multiplicative properties of generalized matrix functions.

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Title: On the multiplicative properties of generalized matrix functions.
Authors: Rodtes, Kijti1 (AUTHOR) kijtir@nu.ac.th
Source: Communications in Algebra. 2026, Vol. 54 Issue 5, p2198-2207. 10p.
Subject Terms: *Matrix functions, *Multiplication, *Positive operators, *Matrix inequalities, *Representations of groups (Algebra), *Symmetry groups
Abstract: For a group G contained in the full symmetric group S n and a character χ of G, the generalized matrix function is defined by d χ G (A) : = ∑ σ ∈ G χ (σ) ∏ i = 1 n A i σ (i) , for all A ∈ M n (C) . In this paper, we utilize the equality case of the inequality | d χ G (AMB ∗) | 2 ≤ d χ G (AMA ∗) d χ G (BMB ∗) which holds for all A , B ∈ M n (C) and all positive definite matrices M ∈ M n (C) to reveal a comprehensive description of the elements of M n (G , χ) : = { A ∈ M n (C) | d ¯ χ G (AX) = d ¯ χ G (A) d ¯ χ G (X) , ∀ X ∈ M n (C) } , where d ¯ χ G denotes the normalization of d χ G . Certain criteria for the equality of d ¯ χ G and det are thus provided. Additional examination of the characterization discloses a *-group generated by the elementary matrices and positive definite matrices contained in the monoid M n (G , χ) . [ABSTRACT FROM AUTHOR]
Database: Academic Search Index
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  Data: On the multiplicative properties of generalized matrix functions.
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  Data: <searchLink fieldCode="AR" term="%22Rodtes%2C+Kijti%22">Rodtes, Kijti</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> kijtir@nu.ac.th</i>
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  Data: <searchLink fieldCode="JN" term="%22Communications+in+Algebra%22">Communications in Algebra</searchLink>. 2026, Vol. 54 Issue 5, p2198-2207. 10p.
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  Data: *<searchLink fieldCode="DE" term="%22Matrix+functions%22">Matrix functions</searchLink><br />*<searchLink fieldCode="DE" term="%22Multiplication%22">Multiplication</searchLink><br />*<searchLink fieldCode="DE" term="%22Positive+operators%22">Positive operators</searchLink><br />*<searchLink fieldCode="DE" term="%22Matrix+inequalities%22">Matrix inequalities</searchLink><br />*<searchLink fieldCode="DE" term="%22Representations+of+groups+%28Algebra%29%22">Representations of groups (Algebra)</searchLink><br />*<searchLink fieldCode="DE" term="%22Symmetry+groups%22">Symmetry groups</searchLink>
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  Data: For a group G contained in the full symmetric group S n and a character χ of G, the generalized matrix function is defined by d χ G (A) : = ∑ σ ∈ G χ (σ) ∏ i = 1 n A i σ (i) , for all A ∈ M n (C) . In this paper, we utilize the equality case of the inequality | d χ G (AMB ∗) | 2 ≤ d χ G (AMA ∗) d χ G (BMB ∗) which holds for all A , B ∈ M n (C) and all positive definite matrices M ∈ M n (C) to reveal a comprehensive description of the elements of M n (G , χ) : = { A ∈ M n (C) | d ¯ χ G (AX) = d ¯ χ G (A) d ¯ χ G (X) , ∀ X ∈ M n (C) } , where d ¯ χ G denotes the normalization of d χ G . Certain criteria for the equality of d ¯ χ G and det are thus provided. Additional examination of the characterization discloses a *-group generated by the elementary matrices and positive definite matrices contained in the monoid M n (G , χ) . [ABSTRACT FROM AUTHOR]
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1080/00927872.2025.2578212
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 10
        StartPage: 2198
    Subjects:
      – SubjectFull: Matrix functions
        Type: general
      – SubjectFull: Multiplication
        Type: general
      – SubjectFull: Positive operators
        Type: general
      – SubjectFull: Matrix inequalities
        Type: general
      – SubjectFull: Representations of groups (Algebra)
        Type: general
      – SubjectFull: Symmetry groups
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      – TitleFull: On the multiplicative properties of generalized matrix functions.
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            – D: 01
              M: 05
              Text: 2026
              Type: published
              Y: 2026
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            – TitleFull: Communications in Algebra
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