How Does Cholesky Factorization Demonstrate Matrix Norm Inequalities?

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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
 
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Thread 'Finding the nth roots of a complex number'

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