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Difference between scalar and vector inequality!


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 


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