work_ethic
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Homework Statement
Let A =[A11 A12; A*12 A22] be Hermitian Positive-definite.
Use Cholesky factorizations
A11 = L1L*1
A22 = L2L*2
A22-A*12 A-111 A12 = L3L*3
to show the following:
||A22-A*12 A-111 A12||2≤||A||2
Homework Equations
The Attempt at a Solution
Using the submultiplicative and triangle inequalities:
||A22||2+||A*12||2 ||A-111||2||A12||2≤||A||2