linear maps, rank

**rayman** · January 27th 2011, 11:49 AM

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 $N\in GL(n,\mathbb{R})$

**FernandoRevilla** · January 27th 2011, 12:16 PM

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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