Extracting a basis with fixed block inside a matrix

Pierre Youssef

doi:10.1016/j.laa.2014.11.016

Extracting a basis with fixed block inside a matrix

Pierre Youssef

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Given U an n×m matrix of rank n whose columns are denoted by (u_j)_j≤m, several authors have already considered the problem of finding a subset σ ⊂ {1,...,m} such that (u_i)_i∈σ span ℝⁿ and √Tr((Σ_i∈σu_iu_i^t)^-1) is minimized. In this paper, we generalize this problem by selecting arbitrary rank matrices instead of rank 1 matrices. Another generalization is considering the same problem while allowing a part of the matrix to be fixed. The methods of selection employed develop into algorithms.

Original language	English (US)
Pages (from-to)	28-38
Number of pages	11
Journal	Linear Algebra and Its Applications
Volume	469
DOIs	https://doi.org/10.1016/j.laa.2014.11.016
State	Published - Mar 15 2015

Keywords

Restricted invertibility
Subset selection

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2014.11.016

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KW - Subset selection

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ER -

Extracting a basis with fixed block inside a matrix

Abstract

Keywords

ASJC Scopus subject areas

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