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 ...

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 ...

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 ...

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 ...

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