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    I'm doing Edexcel FP3 and I'm on eigenvectors and diagonal matricies.

    What I don't get is, when you are reducing a matrix "A" to its diagonal you go through the following steps:

    1.) Produce a matrix "P" from the normalised eigenvectors.
    2.) Transpose the matrix you have just found.
    3.) Use the formula P^TAP = D to find the diagonal matrix.

    ...But we know that the values of the diagonal matrix are the eigenvalues of the matrix "A" so why don't the examples in the book just skip steps 3.) and 2.) and make the matrix "D" from the eigenvalues you find in step 1.)?

    In an exam, would you be expected to go through the whole method?

    Thanks.
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    You need to compute P^{-1}, not P^T.

    You could in theory just write down D from the eigenvalues. But doing the long-winded method is a great way of verifying your solution, as well as giving you practice in matrix multiplication and finding the inverse of a matrix. Also the matrix P is important in some applications, for example you can derive the formula A^k = PD^kP^{-1}. I don't know whether such applications will come up in an A-Level exam paper, but I'm almost certain you'll be expected to write down the full calculation for diagonalising a matrix.
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    :shock:

    I have to admit to being somewhat shocked that this is now A-level, albeit FP3 and only skimming the surface. I don't think we touched this until 2nd yr uni. in my day (decades a go).
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    (Original post by Dragon)
    You need to compute P^{-1}, not P^T.
    That's not what it says in my textbook :p:
    (Original post by Dragon)
    You could in theory just write down D from the eigenvalues. But doing the long-winded method is a great way of verifying your solution, as well as giving you practice in matrix multiplication and finding the inverse of a matrix. Also the matrix P is important in some applications, for example you can derive the formula A^k = PD^kP^{-1}. I don't know whether such applications will come up in an A-Level exam paper, but I'm almost certain you'll be expected to write down the full calculation for diagonalising a matrix.
    That makes sense
    (Original post by ghostwalker)
    :shock:

    I have to admit to being somewhat shocked that this is now A-level, albeit FP3 and only skimming the surface. I don't think we touched this until 2nd yr uni. in my day (decades a go).
    To be fair though it the last part, of the last chapter, of our last further maths module. How long ago were you at uni?
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    (Original post by soutioirsim)
    How long ago were you at uni?
    Decades is an accurate description; I'm not going to elaborate on that.
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    (Original post by ghostwalker)
    Decades is an accurate description; I'm not going to elaborate on that.
    Fair enough :p:
 
 
 
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