Geodesic
On the inversion of the Valiant function of the rank rigidity of a matrix
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 1, Tome 199 (2021), pp. 60-65

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The rank function $\mathrm{rank}(A,k)$ of a matrix $A$ is the minimal rank of a matrix obtained from $A$ by changing no more than $k$ of its entries. For an arbitrary matrix, we obtain an upper boundary of $\mathrm{rank}(A,k)$. For rigid matrices, we establish a smooth lower boundary and a precise formula for $\mathrm{rank}(A,k)$. Alos, we show that the rank function of a rigid matrix inverses its regidity function. For rigid matrices, an interpretation of the inverse function of the rigidity function is given.
Keywords: rigidity function of a matrix, rank function of a matrix, upper boundary, lower boundary, inverse function.
Mots-clés : rigid matrix 
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     author = {B. V. Konoplev},
     title = {On the inversion of the {Valiant} function of the rank rigidity of a matrix},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {60--65},
     publisher = {mathdoc},
     volume = {199},
     year = {2021},
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     url = {http://geodesic.mathdoc.fr/item/INTO_2021_199_a6/}
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B. V. Konoplev. On the inversion of the Valiant function of the rank rigidity of a matrix. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 1, Tome 199 (2021), pp. 60-65. http://geodesic.mathdoc.fr/item/INTO_2021_199_a6/