# Questions tagged [total-unimodularity]

A totally unimodular matrix is a matrix for which every square non-singular submatrix is unimodular.

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### Total unimodular matrices

I am trying to establish the following relationship. If $T$ is a $m \times n$ $TU$ matrix with the property that all rows of $T$ have the same number of non-zero entries and all entries $\geq 0$. Then ...
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### Proving a set has integer extreme points

The hint says to use TU Properties, but I don't know how to express P as a matrix to use the properties Any help is appreciated
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### Checking for integral extreme points of polytopes characterized by non-TUM matrices?

We know that a sufficient condition on $A$ and $b$ for all vertices of $P=\left\{x \in \mathbb{R}^{n} | A x \leq b, x \geq 0\right\}$ to be integral is that $A$ is totally unimodular (TUM) and $b$ is ...
Regarding the proof of Lemma 2: Matrix $A$ is totally unimodular if and only if the matrix $[A |I]$ is TU, I do not understand the first step on permuting square submatrix of B to the desired form. ...