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 January 8th, 2013, 05:52 AM #1 Newbie   Joined: Jan 2013 Posts: 2 Thanks: 0 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
January 8th, 2013, 07:36 AM   #2
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Joined: Jan 2013

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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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January 13th, 2013, 04:29 PM   #3
Math Team

Joined: Sep 2007

Posts: 2,409
Thanks: 6

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

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