Let F be an algebraically closed field and $T : M_{n}(F) \longrightarrow M_{n}(F)$ be a linear transformation. In this paper we show that if T preserves at least one ...

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 ...

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

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 ...