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Eigen values

  1. Jan 2, 2005 #1
    How can i find the eigen value(s) of A - (alpha)I
    where A is an arbitrary matrix ?
  2. jcsd
  3. Jan 2, 2005 #2


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    Your question is ambiguous. Do you mean just find the eigenvalues of A- which would mean solving the equation det(A- alpha*I)= 0 for alpha or do you mean specifically finding eigenvalues of A- alpha*I for a given value of I?
  4. Jan 2, 2005 #3
    sorry, where I is the identity matrix.
    the matrix is C=(A-alpha*I)
    I need to find the eigen values of C
  5. Jan 2, 2005 #4

    matt grime

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    the eigenvalues of any square matrix, call it M, are the roots of the polynomial in x


    although if you know the eigen values of A you know them of C too.
  6. Jan 2, 2005 #5
    yes I know this, but I don't know how to find the eigen value of that paticular matrix (A can be any matrix). The actual question is that I have to prove that lambda is an eigen value of A only if (lamda - alpha) is an eigen value of C
  7. Jan 2, 2005 #6

    matt grime

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    well, that wasn't waht you asked was it?

    t is an eigenvalue of M if and only if M-tI is not invertible.

    let a be alpha
    If C-tI=A-aI-tI is not invertible, then A-(a+t)I is not invertible, can you fill in the blanks?
  8. Jan 2, 2005 #7
    got it. thanks alot :)
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