Thread: find a norm on R2

find a norm on R2 for which||(0,1)||=1=||(1,0)|| but ||(1,1)||=0.000001


hints: ||(a,b)|| = A |a+b|+B|a-b|

by the hints i have A+B=1 and
2A=0.000001
then solved the equations system i get A=0.0000005
B=1-A=0.9999995 then ||(a,b)|| = 0.000001|a+b|+0.9999995 |a-b|

is it the
answers???

Originally Posted by cummings123321

hints: ||(a,b)|| = A |a+b|+B|a-b|, ..., i get A=0.0000005, ..., ||(a,b)|| = 0.000001|a+b|+0.9999995 |a-b|

is it the
answers???[/B]

Everything looks good except that you seem to have slipped at the end, and replaced A with 0.000001 when you had just solved for A, and got A = 0.0000005. Other than that it looks good.