for <math> i = 1,2 </math>, where <math> A </math> is thea rotation matrix (sometimes also known as a proper orthogonal matrix, (i.e., <math>A^{T}A = I, det(A) = +1 </math>). that<math> A </math> transforms vectors in the body fixed frame into the frame of the reference vectors. Among other properties, rotational matrices preserve the length of the vector they operate on. Note that the direction cosine matrix <math> A </math> also transforms the cross product vector, written as,
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Triad proposes an estimate of the direction cosine matrix of<math> interestA </math> as a solution to the linear system equations given by
