Results 221 to 230 of about 58,492 (258)

Reverse order law in C∗-algebras

Applied Mathematics and Computation, 2011
We study equivalent conditions for the reverse order law (a1a2…an)†=an†a1†a1a2…anan††a1† in C∗-algebras. As corollaries, we obtain some recent and special results.
Dijana Mosić, Dragan Djordjevic
exaly   +2 more sources

Reverse order law for the group inverse in rings

Applied Mathematics and Computation, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dijana Mosić, Dragan Djordjevic
exaly   +3 more sources

Further Results on the Reverse Order Law for Generalized Inverses

SIAM Journal on Matrix Analysis and Applications, 2008
The reverse order rule $(AB)^\dag=B^\dag A^\dag$ for the Moore-Penrose inverse is established in several equivalent forms. Results related to other generalized inverses are also proved.
Dragan Djordjevic
exaly   +2 more sources

Triple reverse-order law for weighted generalized inverses

Applied Mathematics and Computation, 2002
\textit{R. E. Hartwig} [Linear Algebra Appl. 76, 241-246 (1986; Zbl 0584.15002)] established the triple reverse-order law for Moore-Penrose inverses involving the computation of some Moore-Penrose inverses. For a given complex matrix \(A\) of size \(m \times n\), the weighted Moore-Penrose is the unique complex matrix \(X\) of size \(n \times m ...
Yimin Wei, Wenyu Sun
exaly   +2 more sources

The reverse order law for the generalized inverse A(2)T,S

Applied Mathematics and Computation, 2004
Let \(A\) be a matrix \(m \times n\) over the complex number field \(\mathbb{C}\), with \(rank\) \(A=n\), and let \(T\) and \(S\) be subspaces of \(\mathbb{C}^{n}\) and \(\mathbb{C}^{m}\) respectively, with dim \(T=\) dim \(S^{\perp }=t\leq r\). Then \(A\) has a \(\{2\}\)-inverse \(A_{T,S}^{(2)}\) such that \(range\) \(A_{T,S}^{(2)}=T\) and \(null ...
Bing Zheng
exaly   +2 more sources

Improvements on the reverse order laws

Mathematische Nachrichten, 2023
AbstractIn many papers concerning properties of generalized inverses in different settings, we can find the results with many redundant instances of assuming regularity of certain elements. We have made an effort to widen the range of applicability of concrete results by considering more general cases of the problems without imposing any such ...
Cvetković Ilić, Dragana, Milenković, Jovana   +1 more
openaire   +2 more sources

On Generalizations of the Reverse Order Law

SIAM Journal on Applied Mathematics, 1974
T. N. E. Greville has shown that the equations $BB^ + A^ * AB = A^ * AB$ and $A^ + ABB^ * A^ * = BB^ * A^ * $ are necessary and sufficient in order that the reverse order law $(AB)^ + = B^ + A^ + $ hold for pseudoinverses of matrices over the field of complex numbers. E. Arghiriade’s results give the more concise formulation that $(AB)^ + = B^ + A^ + $
Barwick, D. T., Gilbert, J. D.
openaire   +2 more sources

Reverse Order Law

2017
The problem of finding the generalized inverse of a product of matrices led to the investigation of the so-called “reverse order law”.
Dragana S. Cvetković Ilić, Yimin Wei
openaire   +1 more source