Vector*Matrix multiplication through Fast Transforms

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I have recently read a paper in which the authors indicated they used a Fast Cosine Transform to implement a Vector*Matrix multiplication. The idea is to decrease complexity when implementing such thing in Digital Circuits.

Anyway the authors just stated so without any further explaination or citations. they just stated that it could be done through fast transforms (e.g FFT or FCT).

I googled a lot to find any links that would explain such idea, but came back empty handed. can somebody explain how this works for me?