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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
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Vandermonde matrices and general position
Not quite what you are asking for but I think these concepts are related.
First: Is it $k\geq n$ or $k\leq n$. Are $S_i$ disjoint?. If $k < n $ There is a property called restricted orthonormality pro …