  In this work, we adapt Sinkhorn-Knopp theorem for rectangular positive maps
$(T:M_k\rightarrow M_m)$. We extend their concepts of support and total support
to these maps. We show that a positive map $T:M_k\rightarrow M_m$ is equivalent
to a doubly stochastic map if and only if $T:M_k\rightarrow M_m$ is equivalent
to a positive map with total support.
  Moreover, if $k$ and $m$ are coprime then $T:M_k\rightarrow M_m$ is
equivalent to a doubly stochastic map if and only if $T:M_k\rightarrow M_m$ has
support.
  This result provides a necessary and sufficient condition for the filter
normal form, which is commonly used in Quantum Information Theory in order to
simplify the task of detecting entanglement. Let $A=\sum_{i=1}^nA_i\otimes
B_i\in M_k\otimes M_m$ be a state and $G_A: M_k\rightarrow M_m$ be the positive
map $G_A(X)=\sum_{i=1}^nB_itr(A_iX)$. We show that $A$ can be put in the filter
normal form if and only if $G_A: M_k\rightarrow M_m$ is equivalent to a
positive map with total support. We prove that any state $A\in M_k\otimes
M_m\simeq M_{km}$ such that $\dim(\ker(A))<k-1$, if $k=m$, and
$\dim(\ker(A))<\min\{k,m\}$, if $k\neq m$, can be put in the filter normal
form.
  Recently, a connection between the capacity of a rectangular positive map
$T:M_k\rightarrow M_m$ and the capacity of a certain square positive map
$\widetilde{T}:M_{mk}\rightarrow M_{mk}$ was noticed. Here, we obtain a deeper
connection between these maps. As a corollary of our main results, we prove
that $T:M_k\rightarrow M_m$ is equivalent to a doubly stochastic map if and
only if $\widetilde{T}:M_{mk}\rightarrow M_{mk}$ is equivalent to a doubly
stochastic map.
