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Math Help - linear maps, rank

  1. #1
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    linear maps, rank

    Let V=V(m,\mathbb{R}) and  W=W(n,\mathbb{R}) and let f be a matrix corresponding to a linear map from V to W. Verify that rankf=rankf^{t}=rank(Mf^{t}N). Gdzie  M\in GL(m,\mathbb{R}) oraz  N\in GL(n,\mathbb{R})
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    One way:

    M(f^t)=[M(f)]^t

    where:

    M(f) : matrix of f with respect to the basis B_V and B_W

    M(f^t) : matrix of f^t with respect to the dual basis B_W^* and B_V^*


    Fernando Revilla
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