Results 1 to 2 of 2

Math Help - Eigen vectors

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

    Eigen vectors

    I need to know how to compute T with respect to the basis b. and i need a way to know where b is a basis consisting of egeinvectors of T.

    Let v= p_1(R), T(a+bx)= (6a-6b)+(12a-11b)x and the basis B={3+4x,2+3x}

    Let V= R^3, T = \begin{pmatrix}\ a \\ b \\ c\end{pmatrix}\ = \begin{pmatrix}\ 3a + 2b - 2c\\ -4a-3b+2c\\-c\end{pmatrix}\

    The basis B= { \begin{pmatrix}\ 0 \\ 1 \\ 1\end{pmatrix}\ \begin{pmatrix}\ 1 \\ -1 \\ 0\end{pmatrix}\ \begin{pmatrix}\ 1 \\ 0 \\ 2 \end{pmatrix}\ }


    general steps will defenitely help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Mar 2008
    Posts
    128
    To determine if a set is a basis for a subspace, you must show that the set meets two out of the three conditions:

    1. S is linearly independent
    2. S is a spanning set for V
    3. S contains exactly k vectors, where k is the dimension of the space you are working in.

    To show that the basis consists of the eigenvectors of T, you need to show that the matrix-vector product of the standard matrix of T and each vector in B is equal to the product of a scalar and the vector.

    Although, I think it would follow directly from proving that the assumed eigenvectors in the set that you have correspond to distinct eigenvalues, because if an n x n matrix consists of n distinct eigenvalues, and you have separate, linearly independent vectors.

    To determine if the vectors in the set are eigenvectors, you must show that T*v where T is the standard matrix of the linear operator and v is a vector in the basis is equal to some scalar times v, for each vector in the set. The scalars would be your eigenvalues.

    Sorry, this may be jumbled...making sense at all?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Eigen values & eigen vectors of a 3 by 3..
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: October 9th 2011, 07:35 AM
  2. Finding unit eigen values and eigen vectors
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 11th 2011, 09:42 AM
  3. what are eigen values and eigen vectors
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 28th 2010, 07:14 AM
  4. Eigen Vectors and eigen values!
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: February 11th 2010, 06:29 AM
  5. Finding Eigen Value and Eigen Vectors
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: December 26th 2008, 03:43 AM

Search Tags


/mathhelpforum @mathhelpforum