Academic Journal
On the multiplicative properties of generalized matrix functions.
| Τίτλος: | On the multiplicative properties of generalized matrix functions. |
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| Συγγραφείς: | Rodtes, Kijti1 (AUTHOR) kijtir@nu.ac.th |
| Πηγή: | Communications in Algebra. 2026, Vol. 54 Issue 5, p2198-2207. 10p. |
| Θεματικοί όροι: | *Matrix functions, *Multiplication, *Positive operators, *Matrix inequalities, *Representations of groups (Algebra), *Symmetry groups |
| Περίληψη: | 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] |
| Βάση Δεδομένων: | Academic Search Index |
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