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# Matrix Interpretation

## Matrix as Linear Transformation

{% embed url="<https://youtu.be/kYB8IZa5AuE>" %}

* Any matrix-vector product is essentially a linear transformation.&#x20;
* Any linear transformation can be seen as a change of basis as well.&#x20;
* So matrix multiplication is basically a linear transformation of a vector or change of basis.&#x20;

$$A^Tb$$ where $$A$$is a matrix and $$b$$is a vector, denotes the projection of $$b$$ on the columns space of $$A$$.

## Matrix as a Projection

{% embed url="<https://gregorygundersen.com/blog/2018/06/26/dot-product/>" %}