Q=\begin{bmatrix}1/\sqrt3&1/\sqrt3&1/\sqrt3\\ Q21&Q22&Q23\\Q31&Q32&1/\sqrt2\end{bmatrix}
\sqrt
2026-03-25 10:53:39.1774436019
How to calculate missing components of rotation matrix?
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$$ A = \left( \begin{array}{ccc} 1&1&1\\ -2&1&1 \\ 0 & -1& 1 \\ \end{array} \right) $$ has positive determinant ( I guess they want that ) and $AA^T$ is diagonal. That is, $A$ can be adjusted to give $Q;$ there is some diagonal matrix, call it $D,$ such that $DA = Q$
Or, you can negate the second row and interchange columns one and two. So, not just one answer to the original question.