rtaylor Posted February 12, 2011 Share Posted February 12, 2011 I would like to express an SPD matrix A as: A = sI + B where B is also SPD, or alternatively as: A = I + B what constraints need to be imposed on B? Please let me know if this question is mot appropriate for this forum. thanks, Russ Link to comment Share on other sites More sharing options...
D H Posted February 13, 2011 Share Posted February 13, 2011 This looks a bit too much like homework, so all I am going to do is give a hint. Let A=sI+B. Then if x is an eigenvector of B it is an eigenvector of A, and vice versa (you will need to prove this). Link to comment Share on other sites More sharing options...
DrRocket Posted February 19, 2011 Share Posted February 19, 2011 This looks a bit too much like homework, so all I am going to do is give a hint. Let A=sI+B. Then if x is an eigenvector of B it is an eigenvector of A, and vice versa (you will need to prove this). Hint #2 : If A is an SPD think abou the simplest form in which it can be expressed by a suitable choice of basis. Link to comment Share on other sites More sharing options...
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