- #1
Shoelace Thm.
- 60
- 0
Homework Statement
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.
Homework Equations
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?