Exercise
 For M in 

 and a diagonal show that
M  jaj  jbj using the upper bound
M  minD DMD which is exact in this case since D has two blocks

Solution Use D  diagfd g
Since DMD is a singular matrix we have from

A
 that

DMD    a da



d b b  pjaj
 jdaj
 jb dj
 jbj



which we want to minimize with respect to d
The solution is d  pjaj jbj which gives
M  pjaj
 jabj  jbj
 jaj  jbj