# How to interpret a 2-D image as a matrix related to a linear transformation between two vector spaces?

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