Decomposition of matrices into commutators of unipotent matrices of index 2 | Zendy

Xin Hou | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Decomposition of matrices into commutators of unipotent matrices of index 2

Author(s) -

Xin Hou

Publication year - 2021

Publication title -

electronic journal of linear algebra

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.447

H-Index - 31

eISSN - 1537-9582

pISSN - 1081-3810

DOI - 10.13001/ela.2021.5641

Subject(s) - unipotent , mathematics , complex matrix , matrix (chemical analysis) , field (mathematics) , decomposition , product (mathematics) , pure mathematics , combinatorics , group (periodic table) , geometry , physics , chemistry , organic chemistry , chromatography , quantum mechanics

Let $\mathbb{C}$ be the complex field. Denote by $\mathrm{SL}_n(\mathbb{C})$ the group of all complex $n\times n$ matrices with determinant $1$. It is proved that every matrix in $\mathrm{SL}_n(\mathbb{C})$ can be decomposed into a product of two commutators of unipotent matrices of index $2$. Moreover, two is the smallest such number.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research