trace of a compact operator

例句：

1. 1. The detective tracedthe criminal to his hideout.
   侦探追踪到了罪犯的藏身之处。
2. 2. She traced her steps back in time to rememberher childhood.
   她追溯自己的足迹，回忆起童年时光。
3. 3. The scientist traced the originof the disease through genetic research.
   科学家通过遗传研究追溯了这种疾病的起源。