相关论文: Generalization of the Sherman-Morrison-Woodbury fo…
An expression for the Moore-Penrose inverse of a matrix of the form M = XNY , where X and Y are nonsingular, has been recently established by Castro-Gonz\'alez et al. [1, Theorem 2.2]. The expression plays an essential role in developing…
The article presents a generalization of Sherman-Morrison-Woodbury (SMW) formula for the inversion of a matrix of the form A+sum(U)k)*V(k),k=1..N).
We investigate the Moore-Penrose pseudoinverse and generalized inverse of a matrix product $A=CR$ to establish a unifying framework for generalized and randomized matrix inverses. This analysis is rooted in first principles, focusing on the…
In this paper we present expressions for the Drazin inverse of the generalized Schur complement $A-CD^{d}B$ in terms of the Drazin inverses of $A$ and the generalized Schur complement $D-BA^{d}C$ under less and weaker restrictions, which…
Under certain conditions, we prove that the Moore-Penrose inverse of a sum of operators is the sum of the Moore-Penrose inverses. From this, we derive expressions and characterizations for the Moore-Penrose inverse of an operator that are…
We give a constructive characterization of matrices satisfying the reverse-order law for the Moore--Penrose pseudoinverse. In particular, for a given matrix $A$ we construct another matrix $B$, of arbitrary compatible size and chosen rank,…
The Moore-Penrose inverse is a genuine extension of the matrix inverse. Given a complex matrix, there uniquely exists another complex matrix satisfying the four Moore-Penrose conditions, and if the original matrix is nonsingular, it is…
An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4} -inverses and the Moore-Penrose inverse of a given rational matrix A is established. Classes A(2, 3)s and A(2, 4)s are characterized in terms of matrix products (R*A)+R* and…
For two positive definite adjointable operators $M$ and $N$, and an adjointable operator $A$ acting on a Hilbert $C^*$-module, some properties of the weighted Moore-Penrose inverse $A^\dag_{MN}$ are established. When $A=(A_{ij})$ is…
This paper establishes exact expressions for the Drazin inverse of the modified tensor $\mathcal A-\mathcal C*_N\mathcal D^D*_N\mathcal B$ via the Einstein product, formulated using the Drazin inverse of $\mathcal A$ and the generalized…
The aim of this work is to characterize linear maps of inner pro\-duct infinite-dimensional vector spaces where the Moore-Penrose inverse exists. This MP inverse generalizes the well-known Moore-Penrose inverse of a matrix $A\in…
In the present paper we investigate Moore-Penrose inverse and characteristic matrix of unbounded WCT operators on the Hilbert space $L^2(\mu)$. Also, we obtain some applications of the Moore-Penrose inverse of unbounded operators on the…
In linear algebra, the sherman-morrison-woodbury identity says that the inverse of a rank-$k$ correction of some matrix can be computed by doing a rank-k correction to the inverse of the original matrix. This identity is crucial to…
In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for physicists dealing, for instance, with optimization problems, with data analysis, with the…
In the general setting of the adjointable operators on Hilbert $C^*$-modules, this paper deals mainly with the weighted Moore-Penrose (briefly weighted M-P) inverse $A^\dag_{MN}$ in the case that the weights $M$ and $N$ are self-adjoint…
In this paper, we first give an expression for the Moore-Penrose inverse of the product of two tensors via the Einstein product. We then introduce a new generalized inverse of a tensor called product Moore-Penrose inverse. A necessary and…
Inversion of operators is a fundamental concept in data processing. Inversion of linear operators is well studied, supported by established theory. When an inverse either does not exist or is not unique, generalized inverses are used. Most…
A Moore--Penrose inverse of an arbitrary complex matrix A is defined as a unique matrix A' such that AA'A=A, A'AA'=A', and AA', A'A are Hermite matrices. We show that this definition has a natural generalization in the context of shortly…
The Sherman-Woodbury-Morrison (SWM) formula gives an explicit formula for the inverse perturbation of a matrix in terms of the inverse of the original matrix and the perturbation. This formula is useful for numerical applications. We have…
Explicit details are presented for calculation of $A^+B$, $A^+AB$ and $AA^+B$ where $A_{m\times n}$ is any nonzero matrix, $A^+$ is the Moore-Penrose pseudoinverse of $A$ and $B$ is any matrix of appropriate dimensions, where the quantities…