My question is,
Is every orthogonal matrix is full rank ?
Is there any specific thorem to answer this question ? I didnt find any
2026-03-28 06:08:27.1774678107
rank of a orthogonal matrix
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If $A$ is orthogonal, then $AA^\top = {\rm Id}_n$, so $(\det A)^2 = 1$. In particular, $\det A \neq 0$, so $A$ is non-singular and hence has full rank.