a simple constructive proof of Simultaneous diagonalization theorem in quantum computing. Firstly，we prove that $AB=BA \Leftrightarrow MM^\dagger=M^\dagger M$: $MM ...

This chapter is concerned with the so-called \emph{diagonalization problem}. For a given linear operator \(\T\) on a \emph{finite}-dimensional vector space \(\V\), we seek answers to the following ...

We extend Donaldson’s diagonalization theorem to intersectionforms with certain local coefficients, under some constraints. Thisprovides new examples of non-smoothable topological 4-manifolds.

Abstract: We trace self-reference phenomena to the possibility of naming functions by names that belong to the domain over which the functions are defined. A naming system is a structure of the form ...

Department of Cyber-Physical Systems, Clark Atlanta University, Atlanta, GA, USA. where P is some reflection (symmetric signed permutation) matrix. Like U, the generalized reflexive matrices A arise ...