Let [ Mn(C) ] denote the set of linear maps from the n × n complex matrices into themselves and let $\hat\Omega_n$ denote the set of complex doubly stochastic matrices, i.e. complex matrices whose row ...

tx and ty are translation. I think a and d are scale and b and c are some function of rotation. I have videos that are flipped and rotated using arbitrary matrices. How can I make them right-side-up ...

In this paper we obtain a linear transformation theorem in which the Radon-Nikodym derivative is very closely related to the transformation. We also obtain a vector-valued conditional version of this ...

This is a subject I struggled with the first time I took it. Ironically, this was the engineering version of it. It wasn't until I took the rigorous, axiomatic version that everything clicked.

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 ...