Four types of Positive-definite Quaternion Matrices and their properties

2015 ◽  
pp. 61-64
Keyword(s):  
Positive Definite ◽  
Quaternion Matrices

scholarly journals Determinantal inequalities of Hua-Marcus-Zhang type for quaternion matrices

2021 ◽  
Vol 19 (1) ◽  
pp. 562-568
Author(s):  
Yan Hong ◽  
Feng Qi
Keyword(s):  
Positive Definite ◽  
Positive Definite Matrices ◽  
Quaternion Matrices ◽  
Determinantal Inequalities

Abstract In this paper, the authors extend determinantal inequalities of the Hua-Marcus-Zhang type for positive definite matrices to the corresponding ones for quaternion matrices.

scholarly journals Positive coincidence points for a class of nonlinear operators and their applications to matrix equations

2020 ◽  
Vol 18 (1) ◽  
pp. 858-872
Author(s):  
Imed Kedim ◽  
Maher Berzig ◽  
Ahdi Noomen Ajmi
Keyword(s):  
Banach Space ◽  
Positive Solution ◽  
Positive Definite ◽  
Positive Cone ◽  
Matrix Equations ◽  
Ordered Banach Space ◽  
Coincidence Points ◽  
Nonlinear Operators ◽  
Nonlinear Matrix

Abstract Consider an ordered Banach space and f,g two self-operators defined on the interior of its positive cone. In this article, we prove that the equation f(X)=g(X) has a positive solution, whenever f is strictly \alpha -concave g-monotone or strictly (-\alpha ) -convex g-antitone with g super-homogeneous and surjective. As applications, we show the existence of positive definite solutions to new classes of nonlinear matrix equations.

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