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December 29th, 2009, 03:51 AM   #1
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Adjoint matrix

I need to prove that for a square matrix (nXn) A: if rkA= n-1 then rk adjA= 1.

Thanks for any help...
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January 29th, 2010, 07:31 AM   #2
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Re: Adjoint matrix

I don't know if this helps, but I looked up the Adjoint matrix on Wikipedia, and found this:

http://en.wikipedia.org/wiki/Adjoint_matrix

So, the adjoint matrix is the conjugate transpose, right? Well then, take the matrix:

(1 0 0)
(0 1 0)
(0 0 0)

The rank of this matrix is 2, which is n - 1. It happens to be self-adjoint, so the rank of the adjoint is also 2, i.e. not 1. I don't think that it's true.
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