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 December 29th, 2009, 03:51 AM #1 Newbie   Joined: Nov 2009 Posts: 15 Thanks: 0 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...
 January 29th, 2010, 07:31 AM #2 Newbie   Joined: Jan 2010 Posts: 8 Thanks: 0 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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# rank of adjoint is 1

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