- #1

- 2

- 0

## Homework Statement

Let A =[A

_{11}A

_{12}; A

^{*}

_{12}A

_{22}] be Hermitian Positive-definite.

Use Cholesky factorizations

A

_{11}= L

_{1}L

^{*}

_{1}

A

_{22}= L

_{2}L

^{*}

_{2}

A

_{22}-A

^{*}

_{12}A

^{-1}

_{11}A

_{12}= L

_{3}L

^{*}

_{3}

to show the following:

||A

_{22}-A

^{*}

_{12}A

^{-1}

_{11}A

_{12}||

_{2}≤||A||

_{2}

## Homework Equations

## The Attempt at a Solution

Using the submultiplicative and triangle inequalities:

||A

_{22}||

_{2}+||A

^{*}

_{12}||

_{2}||A

^{-1}

_{11}||

_{2}||A

_{12}||

_{2}≤||A||

_{2}