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April 23rd, 2013, 10:46 PM  #1 
Newbie Joined: Apr 2013 Posts: 10 Thanks: 0  Not finding one of the eigenvalue
Hi, I have this matrix As the title says, I try to find the eigenvalues for it. I do this by doing: L2 > L2 3/2L1 and L4 > l4  1/2L1 This way I get a triangular matrix like: Then gets a determinant of with leads me to eigenvalues of {2,4,1} However, when I look the answer, I see that, beyond these values, 3 is also a eigenvalue. So what I am missing? Thanks for the help 
April 24th, 2013, 07:30 AM  #2 
Newbie Joined: Apr 2013 Posts: 11 Thanks: 0  Re: Not finding one of the eigenvalue
I checked it with MATLAB. I found out that eigen values are 4,2 and 1 So you are correct other than the signs are just opposite 
April 24th, 2013, 10:33 AM  #3 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Not finding one of the eigenvalue
You seem to be saying that you first rowreduced the matrix, then found the eigenvalues of the rowreduced matrix. You cannot do that the eigenvalues of the row reduced matrix are not necessarily the same as the eigenvalues of the original matrix. What you can can do is expand the eigenvalue determinant by "rows" and 'columns". Expanding on the first row, we have That is now a "triangular" array so its determnant is the product of numbers on the diagonal: . 2 is a double eigenvalue, 1 and 4 are the other eigenvalues. 
April 24th, 2013, 10:46 AM  #4 
Newbie Joined: Apr 2013 Posts: 10 Thanks: 0  Re: Not finding one of the eigenvalue
Hi, HallsofIvy. There is something missing in your latex commands, so I didn't understand what you did in the expansion of the eigenvalue determinant. Can you try to do it again? Thanks to both


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eigenvalue, finding 
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