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 ...

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 ...

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 ...

Annals of Mathematics, a distinguished journal of research papers in pure mathematics, was founded in 1884. Annals of Mathematics is published bimonthly with the cooperation of Princeton University ...

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, ...

The matrix M is based on the Pseudo-Hadamard Transform (PHT) in the original SAFER family of ciphers. The matrix M can be realized as a series of 2-PHT butterflies and Armenian Shuffles ( a kind of ...