Year: 2026
Type: article
Abstract: This paper presents a constructive method for extracting a maximal set of linearly independent rows from a dataset matrix and computing explicit dependency coefficients for dependent rows. The proposed approach incrementally builds an independent subset by preserving linear independence at each step and subsequently derives the coefficient matrix expressing dependent rows as linear combinations of independent rows using a closed-form analytical expression based on the Gram matrix. Unlike classical rank-revealing techniques such as Gaussian elimination or singular value decomposition, which primarily identify independent components, the method directly provides explicit reconstruction relationships between dependent and independent rows. This enables structural analysis of redundancy within datasets and facilitates dimensionality reduction and feature selection. The mathematical formulation, algorithmic procedure, and numerical considerations are presented, demonstrating the effectiveness and interpretability of the approach.
Author: Raphaël Sasportas
Institution: ECAM-EPMI
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7140079945
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