Let $\bf b$ be a column vector and $\bf I$ the identity matrix. Is there in some way for some field of elements that
$${\bf bb}^T = {\bf I}$$
can hold?
2026-04-11 10:58:46.1775905126
Can ${\bf bb}^T = \bf I$ hold for any field?
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Regardless of anything, $bb^T$ has rank $\le1$, because $(bb^T)x=\alpha b$ for the scalar $\alpha=b^Tx$.