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 April 6th, 2010, 12:09 PM #1 Senior Member   Joined: Nov 2009 Posts: 169 Thanks: 0 Find an invertible matrix P Let be a linear transformation T(v) = Av where A = [1 1 3 1] [0 2 2 4] [0 0 3 2] [0 0 1 4] Find the characteristic polynomial of A and compute the eigenvalues of T. Find a basis for each eigenspace. Either find an invertible matrix P and a diagonal matrix D such that or else explain why this is impossible. I know how to find the characteristic polynomial and the eigenvalues of A but not T. June 24th, 2010, 07:13 AM #2 Member   Joined: Jun 2010 Posts: 80 Thanks: 0 Re: Find an invertible matrix P Hello, nice to meet you. I'm new in here. I think your problem resolves to : The eigenvalues and carac. polynomial of A are of T. This, because it can be proven that any representation of T has the same eigenvalues and carac. polynomial : for example : Ax=kx, then I write x=Py a change of basis, and multiply leftly with P^-1 : P^-1APy=ky, where we recognize that P^-1AP=A' is the matrix representing A in the new basis, hence the result. So we can define these quantities intrinsically, in the sense : even if the calculation is made in a basis, the basis has no influence, since a change of basis does not change these results. Tags find, invertible, matrix Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Magnesium Linear Algebra 2 December 11th, 2013 02:09 AM shine123 Linear Algebra 1 September 21st, 2012 08:47 AM problem Linear Algebra 3 August 31st, 2011 05:30 AM paulyc2010 Algebra 4 April 18th, 2010 02:50 PM Victorious Linear Algebra 1 January 5th, 2009 03:54 PM

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