Open AccessThe maximal and minimal ranks of a quaternion matrix expression with applications
Author(s) -
Somaiyeh Rashedi,
Ghodrat Ebadi,
Anjan Biswas
Publication year - 2013
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2013.03.002
Subject(s) - quaternion , mathematics , matrix (chemical analysis) , expression (computer science) , pure mathematics , algebra over a field , computer science , geometry , materials science , composite material , programming language
In this paper, we establish the formulas of the extermal ranks of the quaternion matrix expression f(X1,X2) = C7 − A4X1B4 − A5X2B5 where X1, X2 are variant quaternion matrices subject to quaternion matrix equations A1X1 = C1, A2X1 = C2, A3X1 = C3, X2B1 = C4, X2B2 = C5, X2B3 = C6. As applications, we give a new necessary and sufficient condition for the existence of solutions to some systems of quaternion matrix equations. Some results can be viewed as special cases of the results of this paper