Stable Rank

Stable rank is a mathematical way to measure how "spread out" or "complex" a matrix is, which can represent data or systems. It is calculated as the ratio of the matrix's overall size (its Frobenius norm) to the size of its most significant components (its operator norm). A low stable rank indicates that the matrix is dominated by a few key features or patterns, making it more predictable or compressible. Conversely, a high stable rank suggests the matrix is more complex, containing many diverse features. This concept helps in understanding the structure and complexity of data in fields like data analysis and machine learning.