Abstract
If the determinant of a $3 \times 3$ matrix vanishes and its entries are unimodular complex numbers then two rows or two columns of the matrix are linearly dependent. The proof is remarkably easy. Generalizations include estimates for subdeterminants if the determinant is small and the moduli of the entries are close to $1$.
Citation
Jerzy Browkin. Eduard Wirsing. "Rank two matrices with elements of norm 1." Funct. Approx. Comment. Math. 33 7 - 14, 2005. https://doi.org/10.7169/facm/1538186599
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