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Re: Difference between scalar and vector inequality!

  • To: mathgroup at
  • Subject: [mg52284] Re: Difference between scalar and vector inequality!
  • From: "Steve Luttrell" <steve_usenet at>
  • Date: Sun, 21 Nov 2004 07:23:19 -0500 (EST)
  • References: <cnn1ct$8t4$>
  • Sender: owner-wri-mathgroup at

Here is a counterexample.

Define the a, b, c matrices (2 by 2 is sufficient for a counterexample):


Evaluate the determinants and the two inequalities:


This produces the output:


The |a|, |b| and |c| are all non-negative.
log |i+a| >= log |i+b| is true
log |i+a+c| >= log |i+b+c| is false

BTW you don't need the Log functions above because the logarithm function is 
monotonic and so doesn't affect the inequality test.

Steve Luttrell

"Sungjin Kim" <kimsj at> wrote in message 
news:cnn1ct$8t4$1 at
> 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
> kimsj at

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