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## Main Question or Discussion Point

If I know that [itex]\sum_{k=1}^n a_{ik} = 1[/itex] and [itex]\sum_{j=1}^n b_{kj} = 1[/itex], why is the following permitted?

[tex]\sum_{j=1}^n \sum_{k=1}^n a_{ik}b_{kj} = \left(\sum_{j=1}^n b_{kj}\right) \left(\sum_{k=1}^n a_{ik}\right) = 1\cdot 1 = 1[/tex]

Thanks!

[tex]\sum_{j=1}^n \sum_{k=1}^n a_{ik}b_{kj} = \left(\sum_{j=1}^n b_{kj}\right) \left(\sum_{k=1}^n a_{ik}\right) = 1\cdot 1 = 1[/tex]

Thanks!