Weyl's theorem

Weyl's theorem concerns the relationship between a matrix's eigenvalues (special numbers that reveal key properties) and its approximate versions. It states that if you slightly modify a matrix, the eigenvalues won't change too much—they'll stay within a certain small range of their original values. This theorem is important because it assures stability: small errors or perturbations in data or calculations won't lead to large, unpredictable changes in the eigenvalues, making the analysis and predictions based on these eigenvalues more reliable in applications like physics, engineering, and data science.