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→Example ''p''=3: simpler |
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: <math> \mathbf{0} = [\mathbf{x}_{k}]_{\times} \, \mathbf{A} \, \mathbf{y}_{k} </math> for <math> \, k = 1, \ldots, N </math>
where <math> [\mathbf{x}_{k}]_{\times} </math> is the [[Cross product#Conversion to matrix multiplication|matrix representation of the vector cross product]]. Notice that this last equation is
Each value of ''k'' provides three homogeneous linear equations in the unknown elements of <math> \mathbf{A} </math>. However, since <math> [\mathbf{x}_{k}]_{\times} </math> has rank = 2, at most two equations are linearly independent. In practice, therefore, it is common to only use two of the three matrices <math> \mathbf{H}_{m} </math>, for example, for ''m''=1, 2. However, the linear dependency between the equations is dependent on <math> \mathbf{x}_{k} </math>, which means that in unlucky cases it would have been better to choose, for example, ''m''=2,3. As a consequence, if the number of equations is not a concern, it may be better to use all three equations when the matrix <math> \mathbf{B} </math> is constructed.
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