On page 4 of this article https://arxiv.org/pdf/1608.05735.pdf is defined totally positive grassmanian, then he says that if an element $[z] \in {Gr_ {k, m}}$ is defined by a matrix $z$ full range $k \in{m}$ (without loss of generality we can assume that $z$ has real entries) My questions are: Why $z$ is a matrix and why it can assume that $z$ has real entries?
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Have a look at the answer I have given here and the references herein: (http://math.stackexchange.com/q/1919146) – Jean Marie Oct 03 '16 at 16:39
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alguna otra respuesta por favor. – tomás Oct 03 '16 at 22:54
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You ask for another answer but what is exactly your problem ? That an affine subspace of dimension $k$ in $\mathbb{R}^n$ i.e. an element of the grasmannian $[z] \in {Gr_ {k, m}}$ can be described by a $(n-k) \times k$ matrix ? If this is the case, I advise you first to look at "Plücker coordinates" for the case $k=1$ and $n=3$ (grassmannian of affine straight lines in 3D space) with $2 \times 3=6$ coordinates. – Jean Marie Oct 04 '16 at 05:11