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It is of consequence to note that the Triad method always produces a proper orthogonal matrix irrespective of the handedness of the reference and body vectors employed in the estimation process. This can be shown as follows.
Let us re-write Eq. ({{EquationNote|8}}) in a matrix form given by
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<math>
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</math>
|{{EquationRef|10}}}}
where <math>
\Gamma := \left[ \hat{S} ~ \vdots ~ \hat{M} ~\vdots~ \hat{S} \times \hat{M} \right]
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