Extracting a basis with fixed block inside a matrix

Research output: Contribution to journalArticlepeer-review


Given U an n×m matrix of rank n whose columns are denoted by (uj)j≤m, several authors have already considered the problem of finding a subset σ ⊂ {1,...,m} such that (ui)i∈σ span ℝn and √Tr((Σi∈σuiuit)-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 languageEnglish (US)
Pages (from-to)28-38
Number of pages11
JournalLinear Algebra and Its Applications
StatePublished - Mar 15 2015


  • Restricted invertibility
  • Subset selection

ASJC Scopus subject areas

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


Dive into the research topics of 'Extracting a basis with fixed block inside a matrix'. Together they form a unique fingerprint.

Cite this