Infinity and one norm question

[Visceral]

Hi,

I was wondering why the one and infinity norm of a complex vector x are not equal to the the one and infinity norm of x* (the conjugate transpose of x)? This seems to be true for the 2-norm, but I am not sure why for these other norms.

 

[Office_Shredder]

What is your definition of infinity norm of x^*?

 

[Visceral]

the infinity norm of x* = (x1*, x2*, ... , xn*)^T is

max|xj*| where 1≤j≤n

if that makes sense. Sorry, not good with latex on here. I think I might see now the infinity and one norm of a complex vector x may not be equal. However, they are equal if x is a real vector correct?

 

[economicsnerd]

If z = x+iy is a complex number (x,y\in \mathbb R), then |z^*|= |x-iy| = x^2+ (-y^2)=x^2+y^2=|z|.