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I'm studying symmetric forms, and I'm stuck on understanding the Lagrange Method of Diagonalization. To be specific, when I diagonalize a symmetric matrix I thought that I should find that the elements of the diagonal are the eigenvalues of A (A is the matrix of the form in the canonic basis), but then when I compute the Lagrange method, the elements that are on the diagonal are not eigenvalues of the first matrix (that is, the matrix A). Could anyone try to explain what is so wrong here?

0212user
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  • What book are you using? – Will Jagy Jun 26 '17 at 01:58
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    Meanwhile, if you are doing what I think, they are not the eigenvalues, but they do agree as far as the number of positive valuers, zero values, and negative values. this is https://en.wikipedia.org/wiki/Sylvester's_law_of_inertia – Will Jagy Jun 26 '17 at 02:01
  • oh, well. Here is one I answered twice yesterday https://math.stackexchange.com/questions/2334081/diagonalizing-symmetric-real-bilinear-form/2334144#2334144
    https://math.stackexchange.com/questions/2334081/diagonalizing-symmetric-real-bilinear-form/2335015#2335015     – Will Jagy Jun 26 '17 at 02:03
  • Yes, your comments answer my question, thank you very much !!! – 0212user Jun 28 '17 at 02:13

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