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, 21:17, 7 May 2009→Commentary Note 12.5
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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>
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 the 1-dimensional matrices <math>(\mathfrak{S}^\mathfrak{L})^\mathfrak{W}</math> and <math>\mathfrak{S}^{\mathfrak{L}\mathfrak{W}}</math> are equal — we simply check whether the following equation holds for an arbitrary choice of the index <math>x\!</math> in <math>X.\!</math>
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