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Thread: Eigenvectors

  1. #1 Eigenvectors 
    Forum Ph.D. Heinsbergrelatz's Avatar
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    What is the complex eigenvector for the 2*2 matrice:

    Column 1 = [40,-116], and column 2 = [ 20, -56].

    I have gotten the complex eigenvalues for this matrix which is .

    Will appreciate any help thank you


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  3. #2  
    Forum Professor river_rat's Avatar
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    If you have the eigenvalues already what is the problem?


    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  4. #3  
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    It looks like solving simultaneous equations in 2 unknowns. Av = λv, where A is the known matrix and λ is the eigenvalue. v is the eigenvector.
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  5. #4  
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    Quote Originally Posted by Heinsbergrelatz View Post
    What is the complex eigenvector for the 2*2 matrice:

    Column 1 = [40,-116], and column 2 = [ 20, -56].

    I have gotten the complex eigenvalues for this matrix which is .

    Will appreciate any help thank you
    The whole point of "eigenvalue" and "eigenvector" for matrix A is that for an eigenvalue and v an eigenvector. Given that -8+ 4i is an eigenvalue, a corresponding eigenvector must satisfy . So they must satisfy 40x+ 20y= (-8+ 4i)x, -116x- 56y= (-8+ 4i)y Specifically because -8+ 4i is an eigenvalue, those equations are not independent. There exist an infinite number of eigenvectors corresponding to a single eigenvalue (a subspace of them). What you can do is solve for, say, y in terms of x to get a general formula for the eigenvectors depending on the single parameter, x.
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  6. #5  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    Thank You, so i have solved it, and i got two vectors: [1, -i/5 -12/5], [1, i/5 -12/5] , however it says represent in terms of where c=(_,_) and d= (_,_). Confused what is the c and d in these eigenvectors i have gotten. Help please.

    Thank You
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  7. #6  
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    Quote Originally Posted by Heinsbergrelatz View Post
    Thank You, so i have solved it, and i got two vectors: [1, -i/5 -12/5], [1, i/5 -12/5] , however it says represent in terms of where c=(_,_) and d= (_,_). Confused what is the c and d in these eigenvectors i have gotten. Help please.

    Thank You
    What's wrong with
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  8. #7  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    .... i see.. Thank you !
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  9. #8  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    Question on symmetric matrices, if i have the matrix with the column 1 =[55, -112] and column 2 = [24, -49], how do I find S, D, S^-1 such that ?

    Thank You
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