JIPAM

On the Determinantal Inequalities  
 
  Authors: Shilin Zhan,  
  Keywords: Minkowski inequality, Determinantal inequality, Positive definite matrix, Eigenvalue.  
  Date Received: 24/08/05  
  Date Accepted: 13/09/05  
  Subject Codes:

15A15, 15A57.

  
  Editors: Bicheng Yang,  
 
  Abstract:

In this paper, we discuss the determinantal inequalities over arbitrary complex matrices, and give some sufficient conditions for

$displaystyle d[A + B]^t ge d[A]^t + d[B]^t,$    

where $ t in mathrm{R}$ and $ t ge frac{2 }{n}$. If $ B$ is nonsingular and $ func{Re}lambda (B^{ - 1}A) ge 0$, the sufficient and necessary condition is given for the above equality at $ t = frac{2 }{n}$. The famous Minkowski inequality and many recent results about determinantal inequalities are extended.;


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