Communications in Algebra· 2026Q2
Products of hermitian or skew-Hermitian matrices over division rings with involution
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- Q2SCImago
- 2026year
Short summary
Every non-invertible matrix over a division ring with involution can be written as a product of four Hermitian or skew-Hermitian matrices in any specified order.
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Key points
- Non-invertible matrices over a division ring with involution can be factored into four Hermitian or skew-Hermitian matrices.
- The order of the Hermitian/skew-Hermitian matrices in the factorization can be arbitrarily prescribed.
- Matrices in SLn(D) can also be represented as products of finitely many Hermitian or skew-Hermitian matrices.
- An upper bound is derived for the number of matrices needed for the SLn(D) factorization.
AI-generated from the title and abstract; the full text is not read.
Abstract
Let D be a division ring with involution. In this paper, we investigate conditions under which a square matrix in Mn(D) can be expressed as a product of finitely many Hermitian or skew-Hermitian matrices. Among other results, we prove that every non-invertible matrix in Mn(D) can be written as a product of four matrices, each of which is Hermitian or skew-Hermitian, in any prescribed pattern. We also show that every matrix in SLn(D) can be expressed as a product of finitely many Hermitian or skew-Hermitian matrices, and we derive an upper bound for the required number. Our results improve several known theorems, including those in the recent work [Citation3].
The authors' abstract, as published at the source. Communications in Algebra, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics