I am trying to understand summation notation and there are a few inconsistencies in my head that I would like to clear up.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose C is an m*n matrix and [itex] \vec{x} [/itex] is a 1*m row vector. Then,

[tex] \vec{x}C = \sum_{i} x_{i}C_{ij} = \sum_{i} C_{ij}x_{i} = \sum_{i} {C_{ji}}^Tx_{i} = C^T \vec{x} [/tex]

This is clearly wrong but I'm not sure which operation is wrong. In terms of dimensions it doesn't make sense since [itex] C^T [/itex] is n*m and [itex] \vec{x} [/itex] is 1*m.

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# Summation notation

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