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 ...

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 ...

The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a ...

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 ...

It consists of the linear algebra part of MA212, covering the following topics: Vector spaces and dimension. Linear transformations, kernel and image. Real inner products. Orthogonal matrices, and the ...