Let $M$ be the space of $m \times n$ matrices over $\mathbb{R}$. For each $A$ in $M$ let $A'$ be a fixed submatrix of $A$. Is the function $M \to \mathbb{R}$ defined by $A \mapsto \det(A')$ continuous?
2026-04-17 20:48:10.1776458890
Is the function that maps a matrix to the determinant of a submatrix continuous?
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Yes, it's a polynomial in (some of) the entries of $A$.