Nonsingularity and group invertibility of linear combinations of twok-potent matrices

DOI10.1080/03081080903207932zbMath1204.15009OpenAlexW2015992985MaRDI QIDQ3060031

Xiaoji Liu, Tongping Zhu, Julio Benítez Lopez

Publication date: 30 November 2010

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081080903207932

zbMATH Keywords

ranklinear combinationgroup inversenull space\(k\)-potent matrixnonsingularityrange spacegroup invertibility

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (10)

On nonsingularity of combinations of three group invertible matrices and three tripotent matrices ⋮ On invertibility of combinations of \(k\)-potent operators ⋮ Properties of the combinations of commutative idempotents ⋮ ON THE GROUP INVERSE FOR THE SUM OF MATRICES ⋮ The range and kernel relations of a pair of projections ⋮ Additive results for the group inverse in an algebra with applications to block operators ⋮ On the idempotency, involution and nilpotency of a linear combination of two matrices ⋮ On nonsingularity of combinations of two group invertible matrices and two tripotent matrices ⋮ The core inverses of linear combinations of two core invertible matrices ⋮ On nonsingularity and group inverse of linear combinations of generalized and hypergeneralized projectors

Cites Work

• The nullity and rank of linear combinations of idempotent matrices
• The Drazin inverses of sum and difference of idempotents
• On the norm of idempotents in \(C^*\)-algebras
• The difference and sum of projectors
• Nonsingularity of linear combinations of idempotent matrices
• Constructing projections on sums and intersections
• Additive results for the generalized Drazin inverse
• Invertibility of linear combinations of two idempotents
• Inverting the Difference of Hilbert Space Projections
• Nonsingularity of the Difference of Two Oblique Projectors
• Hilbert space idempotents and involutions
• {k}-Group Periodic Matrices
• Additive results for the generalized Drazin inverse in a Banach algebra
• Some additive results on Drazin inverse

This page was built for publication: Nonsingularity and group invertibility of linear combinations of twok-potent matrices