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 ...

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 ...

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 ...

In this review article, we discuss the synthesis and dynamic nature of macromolecular systems that have mechanically linked polymer chains capable of undergoing a topology transformation driven by a ...

In this third video of our Transformer series, we’re diving deep into the concept of Linear Transformations in Self Attention. Linear Transformation is fundamental in Self Attention Mechanism, shaping ...

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 ...