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: <math> 0 = \mathbf{x}_{k}^{T} \, \mathbf{H}_{m} \, \mathbf{A} \, \mathbf{y}_{k} </math> for <math> \, m = 1, \ldots, M </math> and for <math> \, k = 1, \ldots, N </math>
where <math> \mathbf{H}_{
=== Example ''p''=3 ===
In the case that ''p''=3 the follwing three matrices <math> \mathbf{H}_{
: <math> \mathbf{H}_{1} = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0 \end{pmatrix} </math>, <math> \mathbf{H}_{2} = \begin{pmatrix} 0 & 0 & 1 \\ 0 & 0 & 0 \\ -1 & 0 & 0 \end{pmatrix} </math>, <math> \mathbf{H}_{3} = \begin{pmatrix} 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} </math>
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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 a vector valued equation; the left hand side is the zero element in <math> \mathbb{R}^{3} </math>.
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}_{
The linear dependence between the resulting homogeneous linear equations is a general concern for the case ''p > 2'' and has to be dealt with either by reducing the set of anti-symmeric matrices <math> \mathbf{H}_{k} </math> or by allowing <math> \mathbf{B} </math> to become larger than necessary for determining <math> \mathbf{a} </math>.
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