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Thread: Can I get a check on this eigenvalue problem.

  1. #1
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    Can I get a check on this eigenvalue problem.

    I worked this out and got e) as the answer but was wrong. Can someone check my work. Thank you very much... You guys are wonderful!!
    Can I get a check on this eigenvalue problem.-cev.png
    Can I get a check on this eigenvalue problem.-20171111_151846.jpg
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  2. #2
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    Re: Can I get a check on this eigenvalue problem.

    If you work out the eigenvectors it's pretty simple to show they are independent even though 3 is a repeated eigenvalue.

    So there are 3, not 2, independent eigenvectors, i.e. answer (d)
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    Re: Can I get a check on this eigenvalue problem.

    How do I work out if the two 3's I got are independent of each other?
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    Re: Can I get a check on this eigenvalue problem.

    Quote Originally Posted by thatsmessedup View Post
    How do I work out if the two 3's I got are independent of each other?
    I believe you have to just work out the eigenvectors and check. I'll double check this.

    The number of times an eigenvalue is repeated is called it's algebraic multiplicity.

    The number of independent eigenvectors for a repeated eigenvalue is called it's geometric multiplicity.

    The geometric multiplicity <= the algebraic multiplicity

    If it is less than, then the original matrix is called "defective"

    I'm not seeing any clever test on a matrix other than checking it's eigenvectors for linear independence to determine if it is defective.
    Last edited by romsek; Nov 11th 2017 at 01:55 PM.
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    Re: Can I get a check on this eigenvalue problem.

    Is this what you mean?
    Can I get a check on this eigenvalue problem.-20171111_155401.jpg It wont post up and down and I dont know why.
    Last edited by thatsmessedup; Nov 11th 2017 at 01:58 PM.
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    Re: Can I get a check on this eigenvalue problem.

    Quote Originally Posted by thatsmessedup View Post
    Is this what you mean?
    Click image for larger version. 

Name:	20171111_155401.jpg 
Views:	4 
Size:	925.8 KB 
ID:	38302 It wont post up and down and I dont know why.
    it looks like you correctly came up with $(0,0,1)$ and $(1,1,0)$ for the two eigenvectors associated with the eigenvalue 3.

    These two vectors are pretty clearly linearly independent.

    So those two along with the eigenvector associated with the eigenvalue 1 make up a set of 3 linearly independent eigenvectors.
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    Re: Can I get a check on this eigenvalue problem.

    Quote Originally Posted by thatsmessedup View Post
    Is this what you mean?
    Click image for larger version. 

Name:	20171111_155401.jpg 
Views:	4 
Size:	925.8 KB 
ID:	38302 It wont post up and down and I dont know why.
    You can't rotate the image on the Forum. You're going to have to either recopy it or use a program to rotate the image digitally.

    -Dan
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    Re: Can I get a check on this eigenvalue problem.

    Quote Originally Posted by topsquark View Post
    You can't rotate the image on the Forum. You're going to have to either recopy it or use a program to rotate the image digitally.

    -Dan
    everyone using a PC should have a copy of Irfanview

    It's free and just so useful there's no reason to be without it.
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