Results 1 to 2 of 2

Math Help - Linear Algebra help

  1. #1
    Junior Member
    Joined
    Apr 2008
    From
    Gainesville
    Posts
    68

    Linear Algebra help

    Let V be the vector space of complex numbers over the field r. Define T:V-->V by T(z) = Z', where Z' is the complex conjugate of z.
    Prove that T is linear, and compute [T]_beta, where beta={1,i}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by JCIR View Post
    Let V be the vector space of complex numbers over the field R. Define T:V-->V by T(z) = Z', where Z' is the complex conjugate of z.
    Prove that T is linear, and compute [T]_beta, where beta={1,i}
    T(x+y) = \overline{x+y} = \overline{x}+\overline{y} = T(x) + T(y)
    T(rx) = \overline{rx} = r\overline{x} = rT(x)\,\,\, [\because r \in R, \overline{r} = r]


    Clearly the matrix of the linear transformation T \equiv \begin{pmatrix} 1 & 0 \\0 & -1\end{pmatrix}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: August 1st 2011, 11:00 PM
  2. Basic Linear Algebra - Linear Transformations Help
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: December 7th 2010, 04:59 PM
  3. Replies: 2
    Last Post: December 6th 2010, 04:03 PM
  4. Replies: 7
    Last Post: August 30th 2009, 11:03 AM
  5. Replies: 3
    Last Post: June 2nd 2007, 11:08 AM

Search Tags


/mathhelpforum @mathhelpforum