Weyl's theorem is a fundamental result in linear algebra that relates to the eigenvalues of a compact operator on a Hilbert space. It states that the eigenvalues of such an operator, when arranged in a non-increasing order, converge to zero. This means that, as you consider larger and larger dimensions of the operator, the influence of the eigenvalues diminishes. The theorem also highlights that the eigenvalues can accumulate only at zero, which provides insight into the structure of the operator. This result is significant in various fields, including quantum mechanics and functional analysis, where understanding the behavior of operators is crucial.