Results 271 to 280 of about 5,939 (303)

The core invertibility of a companion matrix and a Hankel matrix

Linear and Multilinear Algebra, 2018
ABSTRACTIn this paper, we show that the lower companion matrix associated with the monic polynomial over a ring with unity is core invertible if and only if there exist solutions x and y to (i) , (ii) , (iii) , (iv)  In addition, some methods of characterizing and computing the core inverse of a Hankel matrix and a Toeplitz matrix over a field are ...
Tingting Li, Jianlong Chen
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Nonlinear invertibility preserving maps on matrix algebras

Linear Algebra and its Applications, 2020
Let \(M_{n}\) be the algebra of all \(n\times n\) matrices over the complex field \(\mathbb{C}\) and let \(A^{t}\) denote the transpose of \(A\in M_{n}\). The first example of a solution to a preserver problem dates back to the year 1897 when Frobenius described the form of all linear maps \(\Phi:M_{n}\rightarrow M_{n}\) that preserve the determinant ...
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A New Matrix Decomposition Method for Inverting the Comrade Matrix

Journal of Mathematical & Computer Applications
Herein,we decompose the Comrade matrix based on its lower triangular L and triangular T factorization to calculate its inverse. We then show the proposed method is efficient with two algorithms.
B Talibi, A Aiat Hadj, D Sarsri
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Invertibility of linear maps preserving matrix invariants

Linear and Multilinear Algebra, 1983
There is a noninvertible linear map preserving a given function iff the function is constant on translates of a subspace. Any group preserving the function preserves the subspace. Hence it is often easy to isolate the cases in which such a noninvertible linear map can exist.
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Generalized inverses of an invertible infinite matrix

Linear and Multilinear Algebra, 2006
Recently, it was shown that, contrary to the case of finite matrices (with real or complex entries) an invertible infinite matrix V could have a Moore–Penrose inverse that is not a classical inverse of V. In this article, we show that V has infinitely many group inverses that are also Moore–Penrose inverses.
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A New Method for Inverting Fermionic Matrix

1986
The Alternate Directions Implicit method is generalized and used to compute quark propagators in quenched QCD. Preliminary results on the chiral properties of the theory and on the spectrum of hadrons agree with those obtained with other approaches.
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Groups of invertible elements of matrix rings

Siberian Mathematical Journal, 1999
Let \({\mathcal O}\subseteq\mathbb{Q}_n\) be an arbitrary finitely generated matrix ring over the rationals. The author presents an algorithmic description of the group of units \(U({\mathcal O})\) of this ring. If \(\mathcal O\) is a matrix ring irreducible over the rationals then the ring is a ring with almost solvable endomorphism group whenever the
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Axis of Evil: An Inverted Threat Matrix

2008
President George W. Bush’s 2002 State of the Union Address greatly expanded the war on terror from a focus on al Qaeda and its Afghan Taliban hosts to three rogue states seeking dangerous weapons of mass destruction: Iraq, Iran, and North Korea. Bush labeled these countries “an axis of evil” that threatened world peace: “By seeking weapons of mass ...
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The biofilm matrix: multitasking in a shared space

Nature Reviews Microbiology, 2022
Hans-Curt Flemming, Eric D Van Hullebusch, Thomas R Neu   +2 more
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Extracellular vesicle–matrix interactions

Nature Reviews Materials, 2023
, Jae-won Shin
exaly