Open AccessAll projection-based commuting solutions of the Yang-Baxter-like matrix equation
Author(s) -
Qixiang Dong,
Jiu Ding
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2110203d
Subject(s) - mathematics , matrix (chemical analysis) , quadratic equation , projection (relational algebra) , pure mathematics , algebra over a field , mathematical analysis , geometry , algorithm , materials science , composite material
We determine all the commuting solutions of the quadratic matrix equation AXA = XAX, which can be expressed in terms of projection matrices. All such solutions have special structures and their building blocks satisfy a system of matrix equations, and our general result extends the previous ones in J. Math. Anal. Appl. 402 (2013), 567-573, Applied Math. Lett. 35 (2014), 86-89, Applied Math. Lett. 64 (2017), 231-234, and Applied Math. Lett. 79 (2018), 155-161.