- #1
evilpostingmong
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Homework Statement
Prove that the sum of any two positive operators on V is positive.
Homework Equations
The Attempt at a Solution
This problem seems pretty simple. But I could be wrong. Should I name two
positive operators T and X such that T=SS* and X=AA*? I have a bad
history of seeing a proof and thinking "wow, this'll be cake" which leads to lazy thinking.
Should I just choose two vectors v1 and v2 and establish two inner products, <SS*v1, v2>+<AA*v1, v2>?
I know that A* is real if X is positive, same goes for S. So <AA*v1, v2>=<Av1, Av2>=<A^2v1, v2>. If I'm
right here, its easy street.