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Say I have a matrix $A \in \mathbb{R}^{n \times m}$ that has a rank of $r$ and a property of any $r$ columns of $A$ are linearly independent. Does this kind of matrix have a special name? Do they have other intriguing properties?

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  • $\begingroup$ I doubt that there's a special name. You could rephrase the property as: all nonzero vectors in $\ker(A)$ have more than $r$ nonzero entries. $\endgroup$ Commented Feb 3, 2023 at 22:28
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    $\begingroup$ This is called the “Kruskal rank” of the matrix, and it comes up frequently when working with tensor decompositions. $\endgroup$ Commented Feb 4, 2023 at 12:44

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