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

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

It is proved that the groupG=SU(n) has a decompositionG=FCF whereF is a maximal abelian subgroup andC is an (n − 1)2 parameter subset of matrices. The result is applied to the problem of absorbing the ...

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 ...