%0 Journal Article
%T Approximate diagonalization of self--adjoint matrices over $C(M)$
%A Yifeng Xue
%J Mathematics
%D 2010
%I arXiv
%X Let $M$ be a compact Hausdorff space. We prove that in this paper, every self--adjoint matrix over $C(M)$ is approximately diagonalizable iff $\dim M\le 2$ and $\HO^2(M,\mathbb Z)\cong 0$. Using this result, we show that every unitary matrix over $C(M)$ is approximately diagonalizable iff $\dim M\le 2$, $\HO^1(M,\mathbb Z)\cong\HO^2(M,\mathbb Z)\cong 0$ when $M$ is a compact metric space.
%U http://arxiv.org/abs/1002.3962v1