December 29th, 2009, 02:51 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= n1 then rk adjA= 1. Thanks for any help... 
January 29th, 2010, 06:31 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 selfadjoint, 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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