[math] Can somebody please help me understand how to get from the matrix after finding the eigenvalu | Mathematics | Page 1

vital stag Nov 27, 2024, 6:22 PM

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i dont understand the multiplication of the top row by j

opal snowBOT Nov 27, 2024, 6:22 PM

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atomic topaz Nov 27, 2024, 6:48 PM

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look at the top row

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gives you -2jx-2y = 0, and so we get x-jy = 0 by multiplying by j then dividing by 2

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then we have x = jy, so take y = 1 then we get x = j

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so (j,1) is one specific eigenvector for the complex eigenvalue

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you only need to look at one of the rows because I belive for complex eigenvalues it'll always give you the conjugate on the other

vital stag Nov 28, 2024, 1:52 PM

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thank you very much, but could you do this question without multiplying the j, eg leaving it as x = y/j, so if y=j, x=1, so vector: (1,j)?

atomic topaz Nov 28, 2024, 6:14 PM

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Sure but I would stay away from dividing by j

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This is very small stuff but just reading it off of j x = y and taking x to be 1 might result in less careless mistakes in the future

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But yes you’re correct

#[math] Can somebody please help me understand how to get from the matrix after finding the eigenvalu