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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

3 votes
0 answers
111 views

Nullspace of a matrix modulo an ideal

Suppose $R$ is a multivariate polynomial ring and $I$ is an ideal in $R$. Let $M$ be a $n\times n$ square matrix with entries in $R$, and suppose that det($M$) lies in $I$. Thus, $M$ has a non-trivia …