# Dot Product as Linear Transformation and Duality of Vector-Linear Transformation

So the physical interpretation of a dot product is related to the projection of one vector over the other and multiplying by the length of the other vector.&#x20;

But how we practically compute dot product is element wise multiplication and summation. \
So the question is **Why does this process of mutiplying the coordinates value and adding them together has to do anything with projection? Ans:**

{% embed url="https://youtu.be/LyGKycYT2v0" %}

## Duality: Linear Transformation and Vector&#x20;

The dual of a vector is the linear transformation is encoded. <=> The dual of a "linear transformation from some space to one dimension" is a certain vector in the space&#x20;

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