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Q: rank $k$ implies nonzero minor of size $k \times k$ but for for the vacuous case of $k=0$

BCLCNote 0: I use 'minor' to refer to both sub-matrix and its determinant. So when you delete row k and column $l$, you get a minor matrix. Its determinant is a minor determinant. Is this statement true for $k=0$ instead of $k=1, ..., \min\{m,n\}$? Proposition: Let $F$ be a field. For any $A \in F^{...

 

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