There are actually two types of digital transformation: linear and exponential. Both are necessary, but most companies fail at the second.

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 ...

More information: Xilin Yang et al, Complex-valued universal linear transformations and image encryption using spatially incoherent diffractive networks, Advanced Photonics Nexus (2024).

Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations. Prereq., APPM 1360 ...

Suitable linear transformations for preliminary data analysis are available when data consist solely of continuous variables or solely of binary variables. When mixtures of variables are observed, ...

We prove that certain linear operators preserve the Pólya frequency property and real-rootedness, and apply our results to settle some conjectures and open problems in combinatorics proposed by Bóna, ...