Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Infinity and one norm question

  1. Jan 29, 2014 #1

    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.
  2. jcsd
  3. Jan 30, 2014 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    What is your definition of infinity norm of x*?
  4. Jan 31, 2014 #3
    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?
  5. Jan 31, 2014 #4
    If [itex]z = x+iy[/itex] is a complex number ([itex]x,y\in \mathbb R[/itex]), then [itex]|z^*|= |x-iy| = x^2+ (-y^2)=x^2+y^2=|z|[/itex].
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook