Results 31 to 40 of about 772 (64)

The Nullity Theorem for Principal Pivot Transform

, 2013
We generalize the nullity theorem of Gustafson [Linear Algebra Appl. (1984)] from matrix inversion to principal pivot transform. Several special cases of the obtained result are known in the literature, such as a result concerning local complementation ...
Brijder, Robert
core   +1 more source

On relationships between two linear subspaces and two orthogonal projectors

Special Matrices, 2019
Sum and intersection of linear subspaces in a vector space over a field are fundamental operations in linear algebra. The purpose of this survey paper is to give a comprehensive approach to the sums and intersections of two linear subspaces and their ...
Tian Yongge
doaj   +1 more source

Estimates of determinants and of the elements of the inverse matrix under conditions of Ostrovskii theorem

, 2000
Abstract and Applied Analysis, Volume 5, Issue 3, Page 137-146, 2000.
Anatolij I. Perov
wiley   +1 more source

Full column rank preservers that preserve semipositivity of matrices

Special Matrices, 2018
Left invertibility preservers on Mm,n(ℝ), m ≥ n, that preserve either semipositivity of matrices or the subset of minimally semipositive matrices are studied. We prove that such maps cannot be degenerate.
Arumugasamy Chandrashekaran, Jayaraman Sachindranath   +1 more
doaj   +1 more source

On the Relative Gain Array (RGA) with Singular and Rectangular Matrices

, 2019
In this paper we identify a significant deficiency in the literature on the application of the Relative Gain Array (RGA) formalism in the case of singular matrices.
Uhlmann, Jeffrey
core   +1 more source

A center of a polytope: An expository review and a parallel implementation

, 1993
International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 209-224, 1993.
S. K. Sen, Hongwei Du, D. W. Fausett
wiley   +1 more source

Invariance property of a five matrix product involving two generalized inverses

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
Matrix expressions composed by generalized inverses can generally be written as f(A−1, A−2, . . ., A−k), where A1, A2, . . ., Ak are a family of given matrices of appropriate sizes, and (·)− denotes a generalized inverse of matrix.
Jiang Bo, Tian Yongge
doaj   +1 more source

Extensions of pseudo-Perron-Frobenius splitting related to generalized inverse AT,S(2)

Special Matrices, 2018
We in this paper define the outer-Perron-Frobenius splitting, which is an extension of the pseudo- Perron-Frobenius splitting defined in [A.N. Sushama, K. Premakumari, K.C.
Huang Shaowu, Wang Qing-Wen, Wu Shuxia, Yu Yaoming   +3 more
doaj   +1 more source

Singular matrices possessing the triangle property

Special Matrices
It is known that the inverse of an invertible real square matrix satisfying the triangle property is a tridiagonal matrix. In this note, results that may be considered as analogues of this assertion are obtained for the Moore-Penrose inverse and the ...
Priya K. Kranthi, Sivakumar K. C.
doaj   +1 more source

Similarity relations and exponential of dual-generalized complex matrices

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023
In this study, taking into account the fundamental properties of dual-generalized complex (DGC) matrices, various types of similarity relations are introduced considering coneigenvalues/coneigenvectors via di erent conjugates.
Gürses Nurten, Şentürk Gülsüm Yeliz
doaj   +1 more source