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Singular Value Decomposition (SVD) of a matrix $A$ (when interpreted as matrix representation of a linear map between $V$ and $W$) can be understood as choosing suitable bases in both $V$ and $W$ such that we get a diagonal $\Sigma$ with singular values, etc.

SVD is also used in image compressing, in which the image is treated as a rectangular matrix. I am wondering, is there a way to interpret the image (matrix) as a representation of certain linear map between some vector spaces?

Thanks,

/bruin

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Obviously, every matrix represents some linear map between two vector spaces. Similarly, every matrix represents some image, so, uninterestingly, every image represents and is represented by some linear map. What you are looking for, maybe, is a natural, or at least meaningful, interesting functor between images and such linear maps. As far as I know, there is no such thing.

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