1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A question in prooving liniar operator

  1. Mar 7, 2008 #1
  2. jcsd
  3. Mar 7, 2008 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I'm not sure what you mean by "for a polynomial". The formula is T(A)= AT- A.

    Perhaps you are thinking that AT is a power? Even if it were, that would still be alright- if you can multiply matrices you can certainly take a matrix to a power- and a product of matrices still represents a linear transformation.

    However, AT is the standard notation for the 'transpose' of a matrix: basically you swap rows and columns. For a 2 by 2 matrix
    [tex]\left[\begin{array}{cc}a & b \\ c & d\end{array}\right]^T= \left[\begin{array}{cc} a & c \\ b & d\end{array}\right][/tex]
    so that
    [tex]\left[\begin{array}{cc}a & b \\ c & d\end{array}\right]^T- \left[\begin{array}{cc}a & b \\ c & d\end{array}\right]= \left[\begin{array}{c c} a & c \\ b & d\end{array}\right]- \left[\begin{array}{cc}a & b \\ c & d\end{array}\right][/itex]
    [tex]= \left[\begin{array}{cc} 0 & c- b \\ b- c & 0\end{array}\right][/tex]
     
    Last edited: Mar 7, 2008
  4. Mar 7, 2008 #3
    no this sign is a little line like a derivative sign
    no way it cant be a T
    ??
     
  5. Mar 8, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    then I have no idea what it means- it's not a standard notation. Does your book give a definition? If not, ask your teacher.
     
  6. Mar 8, 2008 #5
    i trust your judgement probably its a print mistake
    and they ment T
     
  7. Mar 8, 2008 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    It's my vision I'm not sure you should trust! Is this matrix over the real numbers or complex numbers? Sometimes a little "sword" superscript is use to represent the "Hermitian conjugate" where you take the transpose (switch rows to columns) and take the complex conjugate of all entries. Of course, if your matrix has only real number entries, that is the same as the transpose.
     
    Last edited: Mar 8, 2008
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: A question in prooving liniar operator
  1. Proove series question (Replies: 15)

Loading...