- #1

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How can i find the eigen value(s) of A - (alpha)I

where A is an arbitrary matrix ?

where A is an arbitrary matrix ?

- Thread starter himurakenshin
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- #1

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How can i find the eigen value(s) of A - (alpha)I

where A is an arbitrary matrix ?

where A is an arbitrary matrix ?

- #2

HallsofIvy

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- #3

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the matrix is C=(A-alpha*I)

I need to find the eigen values of C

- #4

matt grime

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det(M-xI)

although if you know the eigen values of A you know them of C too.

- #5

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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 Cmatt grime said:the eigenvalues of any square matrix, call it M, are the roots of the polynomial in x

det(M-xI)

- #6

matt grime

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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

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got it. thanks alot :)

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