A note on the nullity theorem

DOI10.1016/j.cam.2005.02.007zbMath1090.65038OpenAlexW1973607237MaRDI QIDQ818170

Raf Vandebril, Marc Van Barel

Publication date: 24 March 2006

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.02.007

zbMATH Keywords

determinantsrankmatrix inversionQR factorizationQR-decompositionstructured rank matrices\(\{pLR-decompositionnullity theoremq\}\)-semiseparable matrices

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Direct numerical methods for linear systems and matrix inversion (65F05) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items

On the closed representation for the inverses of Hessenberg matrices ⋮ Some results on determinants and inverses of nonsingular pentadiagonal matrices

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A theorem on inverses of tridiagonal matrices
• A note on matrix inversion
• Completing a matrix when certain entries of its inverse are specified
• Rank-preserving diagonal completions of a matrix
• Inverses of banded matrices
• Structure ranks of matrices
• Basic matrices.
• Two fast algorithms for solving diagonal-plus-semiseparable linear systems.
• Generalized Hessenberg matrices.
• A divide-and-conquer algorithm for the eigendecomposition of symmetric block-diagonal plus semiseparable matrices
• Complementary basic matrices
• A sparse \({\mathcal H}\)-matrix arithmetic: General complexity estimates
• On inverting a class of patterned matrices
• Matrix Inversion, Its Interest and Application in Analysis of Data
• Inverses of Matrices $\{a_{ij}\}$ which Satisfy $a_{ij} = 0$ for $j > i+p$.
• Gaussian families and a theorem on patterned matrices
• The Interplay of Ranks of Submatrices

This page was built for publication: A note on the nullity theorem