I was given an example from my teacher when he does something like
$$A^TC^{-1}A \gt B^TC^{-1}B \implies A^TA \gt B^TB$$
Where A and B are vectors.
I am curious on how can the inversed matrix C in the middle got cancelled out?
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2If $C$ isn't a positive multiple of the identity, you can't – user251257 Nov 02 '16 at 19:35
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Maybe they were under some operator (like trace, or something else)? – kolobokish Nov 02 '16 at 19:51
1 Answers
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If that's really what your teacher did, it's a mistake.
Try e.g. $$ A = \pmatrix{1\cr 0\cr},\ B = \pmatrix{0\cr 2\cr},\ C^{-1} = \pmatrix{5 & 0\cr 0 & 1\cr}$$
Robert Israel
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