Nonnegative Moore-Penrose Inverse of Gram Matrices in an Indefinite Inner Product Space

In this paper, we derive necessary and sufficient conditions for the nonnegativity of the Moore-Penrose inverse of a Gram matrix defined in an indefinite inner product space using indefinite matrix multiplication. These conditions include the acuteness of a pair of closed convex cones.     

New results for EP matrices in indefinite inner product spaces

In this paper we study J-EP matrices, as a generalization of EP-matrices in indefinite inner product spaces, with respect to indefinite matrix product. We give some properties concerning EP and J-EP matrices and find connection between them. Also, we present some results for reverse order law for Moore-Penrose inverse in indefinite setting. Finally, we deal with the star partial ordering and improve some results given in the “EP matrices in indefinite inner product spaces” (2012), by relaxing some conditions.     

A note on semibounded pairs of inner products

Using the convexity of the 2-dirnensionai field of values we reprove the well-known result that an inner product that is semibounded on the neutral set of an indefinite inner product of arbitrary dimension is so on the whole space. With this field of values approach we can also remedy some errors in the literature on indefinite inner product spaces.     

Numerical study on Moore-Penrose inverse of tensors via Einstein product

Numerical Algorithms - The notation of Moore-Penrose inverse of matrices has been extended from matrix space to even-order tensor space with Einstein product. In this paper, we give the numerical...     

Locality in Free String Field Theory - II

We study the covariant free bosonic string field theory and explore its locality (causality) properties. We find string fields which are strictly local and covariant, but act on an unconstrained Hilbert space with an indefinite inner product. From these we construct observable fields which act on the physical Hilbert space with a definite inner product. These are shown to be approximately local.     

A Family of higher-order convergent iterative methods for computing the Moore-Penrose inverse

In this paper, we extend the iterative method for computing the inner inverse of a matrix proposed in Li and Li [W.G. Li, Z. Li, A family of iterative methods for computing the approximate inverse of a square matrix and inner inverse of a non-square matrix, Applied Mathematics and Computation 215 (2010) 3433-3442] to compute the Moore-Penrose inverse of a matrix, and show that the generated sequence converges to the Moore-Penrose inverse of a matrix in a higher order. The performance of the method is tested on some randomly generated matrices.     

METRIC GENERALIZED INVERSE OF LINEAR OPERATOR IN BANACH SPACE＊＊＊

The Moore-Penrose metric generalized inverse T of linear operator T in Banach space is systematically investigated in this paper. Unlike the case in Hilbert space, even T is a linear operator in Banach Space, the Moore-Penrose metric generalized inverse T is usually homogeneous and nonlinear in general. By means of the methods of geometry of Banach Space, the necessary and sufficient conditions for existence, continuitv, linearity and minimum property of the Moore-Penrose metric generalized inverse T will be given, and some properties of T will be investigated in this paper.     

A variational principle in discrete space–time: existence of minimizers

We formulate a variational principle for a collection of projectors in an indefinite inner product space. The existence of minimizers is proved in various situations.     

Remarks on numerical ranges of operators in spaces with an indefinite metric

The numerical range of an operator on an indefinite inner product space (possibly infinite dimensional) is studied. In particular, operators having bounded numerical ranges are characterized, and the angle points of the numerical range and their connections with eigenvalues are described.

     

Perturbations of Moore–Penrose Metric Generalized Inverses of Linear Operators in Banach Spaces

In this paper,the perturbations of the Moore–Penrose metric generalized inverses of linear operators in Banach spaces are described.The Moore–Penrose metric generalized inverse is homogeneous and nonlinear in general,and the proofs of our results are different from linear generalized inverses.By using the quasi-additivity of Moore–Penrose metric generalized inverse and the theorem of generalized orthogonal decomposition,we show some error estimates of perturbations for the singlevalued Moore–Penrose metric generalized inverses of bounded linear operators.Furthermore,by means of the continuity of the metric projection operator and the quasi-additivity of Moore–Penrose metric generalized inverse,an expression for Moore–Penrose metric generalized inverse is given.     

On Generalized Numerical Ranges of Operators on an Indefinite Inner Product Space

In this article, numerical ranges associated with operators on an indefinite inner product space are investigated. Boundary generating curves, corners, shapes and computer generations of these sets are studied. In particular, the Murnaghan-Kippenhahn theorem for the classical numerical range is generalized.     

Application of Moore-Penrose inverse in deciding the minimal martingale measure

The Moore-Penrose inverse is an important tool in algebra.This paper shows that the MoorePenrose inverse is also an effcient technique in determining the minimal martingale measure if a security price follows a semi-martingale which satisfies some structure condition.We extend a result of Dzhaparidze and Spreij concerning the Moore-Penrose inverse to the case that the Moore-Penrose inverse of any matrix-valued predictable process is still predictable.Furthermore,we obtain an explicit formula of the minimal martingale measure by employing the Moore-Penrose inverse.Specifically,the minimal martingale measure in a generalized Black-Scholes model is found.     

Products of EP elements in reflexive semigroups

The concept of an EP element is generalized to a regular reflexive semigroup with involution. The existence of the Moore-Penrose inverse of an element is discussed, and some results dealing with the product of EP elements are given.     

Additive Maps Preserving Moore-Penrose Inverses of Matrices on Symmetric Matrix Spaces

Suppose F is a field of characteristic not 2. Let M_nF and S_nF be the n × n full matrix space and symmetric matrix space over F, respectively. All additive maps from S_nF to S_nF (respectively, M_nF) preserving Moore-Penrose inverses of matrices are characterized. We first characterize all additive Moore-Penrose inverse preserving maps from S_nF to M_nF, and thereby, all additive Moore-Penrose inverse preserving maps from S_nF to itself are characterized by restricting the range of these additive maps into the symmetric matrix space.     

算子方程基本问题解的再生核稀疏表示

在一个Hilbert空间中通过内积核定义的线性算子对应一个自然的再生核Hilbert空间结构.本文将称其为H-HK结构.这个结构本身内蕴一个基方法,可以解答线性算子的若干最基本的问题,包括确定或刻画其值域空间、解算子方程及解Moore-Penrose伪-(广义-)逆算子问题.在对已存在结果的简要综述之后,本文的目的是建立H-HK结构下的预正交自适应Fourier分解(pre-orthogonal adaptive Fourier decomposition,POAFD)算法.在这个方法之下导出上述3个问题的解的稀疏表示.在逐次跟踪匹配的优化方法论中POAFD的优选原理保证了它在理论上和实用上的最优性.它也具有算法上的可行性.所提供的方法可有效地应用于具体实际问题,包括信号与图像重构、常微分方程、偏微分方程和优化问题的数值解等.     

具有广义分解态射的加权Moore-Penrose逆

研究范畴中态射的加权Moore-Penrose逆,利用态射广义分解的性质给出了态射加权Moore-Penrose逆存在的一些充要条件,导出了态射的加权Moore-Penrose逆的表达式,推广了态射Moore-Penrose逆的相应结果.     

On oblique projection, rank additivity and the moore-penrose inverse of the sum of two matrices

The existence of certain oblique projectors is revealed by deriving onto-and along-space of a specific projector, namely the Moore-Penrose inverse of the product of two orthogonal projectors. The results are used to create a formula for the Moore-Penrose in-verse of the sum of two rank additive matrices, and to demonstrate relationships with already known facts.     

Generalized inverses of circulant and generalized circulant matrices

An expression for the Moore-Penrose inverse of certain singular circulants by S.R. Searle is generalized to include all circulants. Similar expressions are given for the Moore-Penrose inverse of block circulants with circulant blocks, level-q circulants, k-circulants where |k|=1, and certain other matrices which are the product of a permutation matrix and a circulant. Expressions for other generalized inverses are given.