Changes

|}

|}

If <math>\mathfrak{A}</math> and <math>\mathfrak{B}</math> are two 1-dimensional matrices over the same index set <math>X,\!</math> then <math>\mathfrak{A} = \mathfrak{B}</math> if and only if <math>\mathfrak{A}_x = \mathfrak{B}_x</math> for every <math>x \in X.</math>  Therefore, a routine way to check whether the 1-dimensional matrices <math>(\mathfrak{S}^\mathfrak{L})^\mathfrak{W}</math> and <math>\mathfrak{S}^{\mathfrak{L}\mathfrak{W}}</math> are equal is to check whether the following equation holds for an arbitrary choice of the index <math>x \in X.</math>

If <math>\mathfrak{A}</math> and <math>\mathfrak{B}</math> are two 1-dimensional matrices over the same index set <math>X,\!</math> then <math>\mathfrak{A} = \mathfrak{B}</math> if and only if <math>\mathfrak{A}_x = \mathfrak{B}_x</math> for every <math>x \in X.</math>  This provides us with a routine way of checking whether <math>(\mathfrak{S}^\mathfrak{L})^\mathfrak{W} = \mathfrak{S}^{\mathfrak{L}\mathfrak{W}}</math>, and that is simply to check whether the following equation holds for an arbitrary choice of the index <math>x\!</math> in <math>X.\!</math>

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

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