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January 8th, 2013, 05:52 AM   #1
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Eigen values for nxn matrix

Hi all

I am looking for eigen values of two NxN tridiagonal matrix

My first matrix
1) "1-2a" on the main diagonale except last component -> "1-a"
2) "a" on the upper and lower diagonal
3) all others = 0

Second matrix
1) "1+2a" on main diagonale except last -> "1+3a"
2) "-a" on upper and lower
3) all other =0

I don't know how i can found a formula to know these eigen values
because i am a beginner for this kind of things and because the NxN size is a problem for me.

I think that there is a simple solution because on the web i have found solution (without explications )
For 2 matrix very close (all is similar except the fact that last conponant is different from other in main diagonal)

I will very happy if you could help me for this problem
Thanks
didierB is offline  
 
January 8th, 2013, 07:36 AM   #2
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Re: Eigen values for nxn matrix

i have found this on the net (cf. attachment)

do you know how we can demonstrate this ?
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File Type: jpg eigen.jpg (11.3 KB, 391 views)
didierB is offline  
January 13th, 2013, 04:29 PM   #3
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Re: Eigen values for nxn matrix

Quote:
Originally Posted by didierB
Hi all

I am looking for eigen values of two NxN tridiagonal matrix

My first matrix
1) "1-2a" on the main diagonale except last component -> "1-a"
2) "a" on the upper and lower diagonal
3) all others = 0

Second matrix
1) "1+2a" on main diagonale except last -> "1+3a"
2) "-a" on upper and lower
3) all other =0

I don't know how i can found a formula to know these eigen values
because i am a beginner for this kind of things and because the NxN size is a problem for me.

I think that there is a simple solution because on the web i have found solution (without explications )
For 2 matrix very close (all is similar except the fact that last conponant is different from other in main diagonal)
By "2 matrix" do you mean a 2 by 2 matrix? And "very close" to what?

Quote:
I will very happy if you could help me for this problem
Thanks
HallsofIvy is offline  
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