Related papers: Moore-Penrose Inverse of some Linear Maps on Infin…
The Moore-Penrose inverse of a matrix has been extensively investigated and widely applied in many fields over the past decades. One reason for the interest is that the Moore-Penrose inverse can succinctly express some important geometric…
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…
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 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…
The Moore-Penrose algorithm provides a generalized notion of an inverse, applicable to degenerate matrices. In this paper, we introduce a covariant extension of the Moore-Penrose method that permits to deal with general relativity involving…
In this paper we characterize Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space using indefinite matrix multiplication. This characterization includes the acuteness (or obtuseness) of…
This paper first introduces a new generalized inverse in Minkowski space, called the m-DMP inverse, and discusses its algebraic and geometrical properties. The second objective is to characterize the m-DMP inverse equivalently by ranges,…
We develop the first stochastic incremental method for calculating the Moore-Penrose pseudoinverse of a real matrix. By leveraging three alternative characterizations of pseudoinverse matrices, we design three methods for calculating the…
In this paper, we introduce new representation and characterization of the weighted core inverse of matrices. Several properties of these inverses and their interconnections with other generalized inverses are also explored. Through…
We present explicit formulas for Moore-Penrose inverses of some families of set inclusion matrices arising from sets, vector spaces, and designs.
In this article we provide a fast computational method in order to calculate the Moore-Penrose inverse of singular square matrices and of rectangular matrices. The proposed method proves to be much faster and has significantly better…
We present more than 50 results including some range inclusion results to characterize reverse order law for Moore-Penrose inverse of closed range Hilbert space operators. We use basic properties of Moore-Penrose inverse to prove the…
In this paper, necessary and sufficient conditions are given for the existence of Moore-Penrose inverse of a product of two matrices in an indefinite inner product space (IIPS) in which reverse order law holds good. Rank equivalence…
Many neural learning algorithms require to solve large least square systems in order to obtain synaptic weights. Moore-Penrose inverse matrices allow for solving such systems, even with rank deficiency, and they provide minimum-norm vectors…
The well-known M-P (Moore-Penrose) pseudoinverse is used in several linear-algebra applications; for example, to compute least-squares solutions of inconsistent systems of linear equations. Irrespective of whether a given matrix is sparse,…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
Reverse order law for the Moore-Penrose inverses of tensors are useful in the field of multilinear algebra. In this paper, we first prove some more identities involving the Moore-Penrose inverse of tensors. We then obtain a few necessary…
A common optimization problem is the minimization of a symmetric positive definite quadratic form $< x,Tx >$ under linear constrains. The solution to this problem may be given using the Moore-Penrose inverse matrix. In this work we extend…
In this article we explore several aspects concerning to the Moore-Penrose inverse of a bounded linear operator. On the one hand, we study monotonicity properties of the Moore-Penrose inverse with respect to the L\"owner, star, minus, sharp…
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…