Richard Sinkhorn, Linear Transformations Under Which the Doubly Stochastic Matrices are Invariant, Proceedings of the American Mathematical Society, Vol. 27, No. 2 (Feb., 1971), pp. 213-221 ...

Lord it's been a while since Linear Algebra. IIRC you multiply your source matrix by the inverse of the transformation matrix to restore the source to it's original state. Edit: ahh, here you go ...

Two linear models with error structure of the nested type are considered. Transformations are presented by which uncorrelated errors with constant variances are ...

Transforming light: illustration of how an arbitrary linear transform can be achieved in an all-optical system using diffractive surfaces (Courtesy: Ozcan Lab/UCLA) Researchers in the US have shown ...

So far, researchers have successfully designed monochromatic, or single wavelength illumination, diffractive networks for implementing a single linear transformation (matrix multiplication) operation.

Linear Algebra Vector spaces, linear transformation, matrix representation, inner product spaces, isometries, least squares, generalised inverse, eigen theory, quadratic forms, norms, numerical ...