matrixrich

Matrixrich is a descriptive term used in mathematics, data science, and related fields to characterize a matrix or matrix-like dataset that is richly populated with information. In common usage it refers to matrices that exhibit high nonzero density, diverse numerical values, or substantial linear independence among rows and columns.

There is no single formal definition of matrixrich; it varies by context. It generally implies that the matrix carries a dense structure or a wide range of values that supports expressive representations of data or models.

Key properties often associated with matrixrich objects include a high density of nonzero entries, a broad spectrum of singular values, and high rank relative to size. Such matrices can be easier to approximate with dense low-rank models but more demanding to store and process than sparse matrices.

Examples include the weight matrices of densely connected neural networks, dense adjacency matrices of graphs with strong connectivity, and data matrices derived from measurements with many overlapping features.

In practice, matrixrich structures are valued when modeling capacity and expressiveness outweigh storage costs. They influence algorithm choice, favoring dense linear algebra routines and high-performance computing resources. The term has appeared in academic papers and industry discussions since the early 21st century.