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 ...

The traditional linear transformation model assumes a linear relationship between the transformed response and the covariates. However, in real data, this linear relationship may be violated. We ...

This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American I was enchanted with the words metonymy and ...

Two vectors of information are needed to produce the optimally scaled variable: the initial variable scaling vector x and the target vector y. For convenience, both vectors are first sorted on the ...

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

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 ...