GitHub

2024-12-26-matrix-rank.markdown

In the theory of vector spaces, a set of vectors is said to be linearly independent if there exists no nontrivial linear combination of the vectors that equals the zero vector. If such a linear ...
University of Waterloo

Math 136: Linear Algebra 1

Topics include systems of linear equations, matrix algebra, elementary matrices, and computational issues. Other areas of the course focus on the real n-space, vector spaces and subspaces, basis and ...
IEEE

Matrix full rank, Controllability and Observability: Revisit Basic Concepts

Abstract: In control theory using the state-space method, it is often assumed that a matrix is of full rank to further mathematical development. Few people stop to ask two questions: (1) How far is ...
GitHub

A Python demonstration of speeding up matrix multiplication and reducing memory using a quantum-inspired low-rank SVD trick, with examples in AI.

This repository demonstrates a powerful, classical linear algebra technique—low-rank approximation via Singular Value Decomposition (SVD)—to dramatically accelerate common matrix operations like GEMM ...
University of Waterloo

On the Complexity of Robust PCA and l1-Norm Low-Rank Matrix Approximation

Gillis, N. , & Vavasis, S. A. . (2018). On the Complexity of Robust PCA and l1-Norm Low-Rank Matrix Approximation. Mathematics of Operations Research, 43, 1072-1084.
IEEE

Non-Stationary Channel Estimation for XL-MIMO With Hybrid Structure via Low-Rank Matrix Completion

Abstract: Due to the spatial non-stationary (SnS) property of extremely large-scale MIMO (XL-MIMO), channel estimation algorithms that rely on the assumption of spatial stationarity are no longer ...