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 Question concerning Aldrovandi/Freitas-article Gottfried Ultimate Fellow Posts: 790 Threads: 121 Joined: Aug 2007 01/19/2008, 09:10 AM (This post was last modified: 01/19/2008, 11:35 AM by Gottfried.) andydude Wrote:So what is the difference between "normality" and "distinct eigenvalues"? I thought that distinct eigenvalues were sufficient for diagonizability... Andrew Robbins "normal": let M be a matrix (we're discussing real matrices for example). Then M is "normal", if M commutes with its transpose M*M' = M'*M This equality is obviously true for symmetric M, but also for some others. It is said, that for normal matrices, if T*M*T^-1 = D , D diagonal, then T is orthogonal, meaning T*T' = T*T^-1=I (I think T is always a rotation) and also T*M*T' = D (from other context I'm used to denote rotation-matrices by letter T) --------------------------- not "normal", but still diagonalizable (the more general case): W*M*W^-1 = D no specific properties on W. Related to current discussion: if M is triangular (and diagonalizable), I think W is also triangular (but I must check this), and the eigenvalues are the entries of its diagonal. ------------------- The question whether eigenvalues are distinct or not is not relevant here; this is only relevant for the description of further properties of W (whether it is unique ... ) Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread Question concerning Aldrovandi/Freitas-article - by Gottfried - 01/18/2008, 10:28 PM RE: Question concerning Aldrovandi/Freitas-article - by bo198214 - 01/19/2008, 06:30 AM RE: Question concerning Aldrovandi/Freitas-article - by andydude - 01/19/2008, 08:31 AM RE: Question concerning Aldrovandi/Freitas-article - by bo198214 - 01/19/2008, 08:38 AM RE: Question concerning Aldrovandi/Freitas-article - by Gottfried - 01/19/2008, 09:10 AM

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