Difference between scalar and vector inequality!

*To*: mathgroup at smc.vnet.net*Subject*: [mg52276] Difference between scalar and vector inequality!*From*: "Sungjin Kim" <kimsj at mobile.snu.ac.kr>*Date*: Sat, 20 Nov 2004 03:41:53 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

The following inequality under given condition is true for scalar. However, is this still true for matrix? log| I + A + C| >= log| I + B + C| if log| I + A| >= log| I + B| and A, B, C >= 0 where |A| is absolute and determinant for scalar and matrix, respectively, and A >= 0 means semi positive scalar or semi positive definite matrix, respectively. Furthermore, is it possible to prove it using our Mathematica? Thank you in advance. Br, - Sungjin Kim communication at samsung.com kimsj at mobile.snu.ac.kr

**Follow-Ups**:**Re: Difference between scalar and vector inequality!***From:*DrBob <drbob@bigfoot.com>