V, W, XE Cnan are Hermitian and T = VW W*X is positive semi definite. 1....

 

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V, W, XE Cnan are Hermitian and T = VW W*X is positive semi definite. 1. Show Vr, s € Cn: (r* Vr) (s* Xs) ≥ |s*Wr|² 2. If V is positive semi definite, show Vr, s E Cn (r* Vr) (s* Vs) ≥ |s*Vr| using part 1. 3. If V is positive definite, show that Vr, s € Cn (r* Vr) (s*V−¹s) ≥ |s* Inr|² using 1. and 2. V, W, XE Cnan are Hermitian and T = VW W*X is positive semi definite. 1. Show Vr, s € Cn: (r* Vr) (s* Xs) ≥ |s*Wr|² 2. If V is positive semi definite, show Vr, s E Cn (r* Vr) (s* Vs) ≥ |s*Vr| using part 1. 3. If V is positive definite, show that Vr, s € Cn (r* Vr) (s*V−¹s) ≥ |s* Inr|² using 1. and 2.

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