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The fact that <math>\mathit{l}^\mathrm{w}\!</math> denotes the elements of a subset of <math>X\!</math> means that the matrix <math>\mathfrak{L}^\mathfrak{W}</math> is a 1-dimensional array of coefficients in <math>\mathbb{B}</math> that is indexed by the elements of <math>X.\!</math>  The value of the matrix <math>\mathfrak{L}^\mathfrak{W}</math> at the index <math>a \in X</math> is written <math>(\mathfrak{L}^\mathfrak{W})_a</math> and computed as follows:

The fact that <math>\mathit{l}^\mathrm{w}\!</math> denotes the elements of a subset of <math>X\!</math> means that the matrix <math>\mathfrak{L}^\mathfrak{W}</math> is a 1-dimensional array of coefficients in <math>\mathbb{B}</math> that is indexed by the elements of <math>X.\!</math>  The value of the matrix <math>\mathfrak{L}^\mathfrak{W}</math> at the index <math>u \in X</math> is written <math>(\mathfrak{L}^\mathfrak{W})_u</math> and computed as follows:

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{| align="center" cellspacing="6" width="90%"

| height="60" | <math>(\mathfrak{L}^\mathfrak{W})_a ~=~ \prod_{x \in X} \mathfrak{L}_{ax}^{\mathfrak{W}_{x}}</math>

| height="60" | <math>(\mathfrak{L}^\mathfrak{W})_u ~=~ \prod_{x \in X} \mathfrak{L}_{ux}^{\mathfrak{W}_{x}}</math>

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The meaning of a formula like that is more easily grasped with the aid of a freely chosen example and a picture of the relations involved.

The meaning of an abstract formula of this kind is more easily grasped with the aid of a freely chosen example and a picture of the relations involved.

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{| align="center" cellspacing="6" width="90%"

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<pre>

<pre>

1   2   3   4   5   6   7   8   9    

a   b   c   d   e   f   g   h   i    

o  o  o  o  o  o  o  o  o  X

o  o  o  o  o  o  o  o  o  X

             |      |                 

             |      |                 

   \ / \ /    \ /    \ / \ /       

   \ / \ /    \ /    \ / \ /       

o  o  o  o  o  o  o  o  o  X

o  o  o  o  o  o  o  o  o  X

1   2   3   4   5   6   7   8   9    

a   b   c   d   e   f   g   h   i    

</pre>

</pre>

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