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Inverse problems involve for example reconstruction of an object based on physical measurements and finding a best model/parameters out of a family given observed data. Typically the corresponding "forward" problems are well-posed and can be solved straightforwardly, while the inverse problems are often ill-posed. Not to be confused with the (inverse) tag.
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An explicit reconstruction of a matrix from its minors
Assume for simplicity that $kl=d+1$.
Then I claim that $V \otimes \det V$ appears as a summand of $\left( \bigwedge^k V\right)^{\otimes l}$ with multiplicity $l-1$.
The maps $\left( \bigwedge^k V\ri …