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Note that computational efficiency has been achieved in this procedure by replacing the matrix inverse with a transpose. This is possible because the matrices involved in computing attitude are each composed of a triad of [[Orthonormality|orthonormal]] basis vectors. "TRIAD" derives its name from this observation.
==Triad Attitude Matrix and
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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