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

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 ...

Abstract: In this paper we prove the discrete convolution theorem by means of matrix theory. The proof makes use of the diagonalization of a circulant matrix to show that a circular convolution is ...

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