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Square Root of Positive Operator

  1. Apr 12, 2013 #1
    1. The problem statement, all variables and given/known data
    Suppose [itex] U = T^2 + \alpha T + \beta I [/itex] is a positive operator on a real inner product space V with [itex] \alpha^2 < 4 \beta [/itex] . Find the square root operator S of U.


    2. Relevant equations



    3. The attempt at a solution
    Isn't this just the operator [itex] S \in L(V) [/itex] such that [itex] S e_k = \sqrt{ \lambda_k } e_k [/itex], where the [itex] e_k [/itex] form an orthonormal basis of eigenvectors of U? Can we get anymore specific here than the definition?
     
  2. jcsd
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