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This must be a very basic question, but since i've just started diving into linear algebra, it's sort of new to me.

Matrix multiplication has a rule: given matrices $\mathbf{A} \in \mathbb{R}^{j\times k}$ and $\mathbf{B}\in \mathbb{R}^{l \times m}$, the multiplication can only occur if $k = l$, and there will be a resulting matrix $C \in \mathbb{R}^{j \times m}$.

This also applies to dot product? I couldn't really get the difference between these two operations.

Thanks.

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    $\begingroup$ Yes the same will apply to dot products. Geometrically, dot products measure angles between vectors, but you can only do that if the vectors live in the same space ($\Bbb{R}^n$ vs $\Bbb{R}^m$). If they don't live in the same space, it doesn't make sense to ask for an angle between the two. $\endgroup$ Dec 7 '20 at 16:50
  • $\begingroup$ Thanks. I'm getting so much confused about this operations in the area of neural networks, where there are matrices operations between inputs and weights. $\endgroup$
    – joann2555
    Dec 7 '20 at 16:54

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