Eigen values

  • #1
How can i find the eigen value(s) of A - (alpha)I
where A is an arbitrary matrix ?
 

Answers and Replies

  • #2
HallsofIvy
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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?
 
  • #3
sorry, where I is the identity matrix.
the matrix is C=(A-alpha*I)
I need to find the eigen values of C
 
  • #4
matt grime
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the eigenvalues of any square matrix, call it M, are the roots of the polynomial in x

det(M-xI)

although if you know the eigen values of A you know them of C too.
 
  • #5
matt grime said:
the eigenvalues of any square matrix, call it M, are the roots of the polynomial in x

det(M-xI)
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
 
  • #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?
 
  • #7
got it. thanks alot :)
 

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