•  
  •  
 

Keywords

Determinantal inequality, Positive definite matrix

Abstract

Let A, B, C be n × n positive semidefinite matrices. It is known that det(A + B + C) + det C ≥ det(A + C) + det(B + C), which includes det(A + B) ≥ det A + det B as a special case. In this article, a relation between these two inequalities is proved, namely, det(A + B + C) + det C − (det(A + C) + det(B + C)) ≥ det(A + B) − (det A + det B).

Share

COinS
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.