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Equivalent bases for Vector Spaces over Complexes.

  1. May 5, 2010 #1

    WWGD

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    Hi:

    Given a fin.dim vector space V over R, and two different bases B_V,B_V'

    for V , we say that B_V,B'_V are equivalent as bases ( or have the same

    orientation) , if there exists a matrix T with TB=B', and DetT>0.

    How do we define equivalent bases for vector spaces over the

    Complexes.?. If W is a vector space over C, and we are given

    bases B_W, B'_W , then the matrix L with LB=B' may not have

    a real-valued determinant.

    Is there then a way of defining equivalent bases in the second case.?

    Thanks.
     
  2. jcsd
  3. May 6, 2010 #2

    lavinia

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    I think all bases are equivalent in a complex vector space because the the general linear group over the complex numbers is path connected.
     
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