matrix square root

Discussion in 'Undergraduate Math' started by Jeremy Watts, Jan 7, 2006.

  1. Jeremy Watts

    Jeremy Watts Guest

    I know that the square root of a matrix can be found be firstly
    performing an eigen decomposition , so that the matrix appears in the
    form A = PDP^ -1 , and then from this the square root of A is given by
    PD^1/2 P^ -1

    But what if the matrix cannot be diagonalised? Can the square root of
    a matrix be found in this instance?
    Jeremy Watts, Jan 7, 2006
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  2. Jeremy Watts

    Virgil Guest

    Sometimes, but not always.

    [[ a 1]
    [ 0 a]] , for a <> 0 has a square root, but for a = 0 does not,

    and is not diagonizable in either case.
    Virgil, Jan 8, 2006
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