Related papers: Moore-Penrose Dagger Categories
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 this paper, we investigate *-DMP elements in $*$-semigroups and $*$-rings. The notion of *-DMP element was introduced by Patr\'{i}cio in 2004. An element $a$ is *-DMP if there exists a positive integer $m$ such that $a^{m}$ is EP. We…
Generalized inverses of tensors play increasingly important roles in computational mathematics and numerical analysis. It is appropriate to develop the theory of generalized inverses of tensors within the algebraic structure of a ring. In…
The classes of 1MP-inverses and MP1-inverses are recently introduced classes of generalized inverses of complex matrix. Actually, they coincide with the classes of $\{1,2,3\}$ and $\{1,2,4\}$ inverses, respectively. We consider these…
One of the fundamental research problems in the theory of generalized inverses of matrices is to establish reverse order laws for generalized inverses of matrix products. Under the assumption that $A$, $B$, and $C$ are three nonsingular…
We provide a categorical proof of convergence for martingales and backward martingales in mean, using enriched category theory. The enrichment we use is in topological spaces, with their canonical closed monoidal structure, which encodes a…
Dagger categories are an essential tool for categorical descriptions of quantum physics, for example in categorical quantum mechanics and unitary topological field theory. Their definition however is in tension with the ``principle of…
Within the context of an involutive monoidal category the notion of a comparison relation is identified. Instances are equality on sets, inequality on posets, orthogonality on orthomodular lattices, non-empty intersection on powersets, and…
In this paper, new block representations of Moore-Penrose inverses for arbitrary complex $2\times2$ block matrices are given. The approach is based on block representations of orthogonal projection matrices.
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 paper, some more properties of the generalized principal pivot transform are derived. Necessary and sufficient conditions for the equality between Moore-Penrose inverse of a generalized principal pivot transform and its…
In this paper, we introduce a ring isomorphism between the Clifford algebra $C\ell_2$ and a ring of matrices, and represent the elements in $C\ell_2$ by real matrices. By such a ring isomorphism, we introduce the concept of the…
We will discuss two approaches to estimating partial derivatives and the metric components; one utilizing past work describing a causal set $\Box$ operator, and one using a construction from linear algebra called the Moore-Penrose inverse.…
In this article we present a new characterization of inverse M-matrices, inverse row diagonally dominant M-matrices and inverse row and column diagonally dominant M-matrices, based on the positivity of certain inner products.
This paper discusses the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, which arises in the numerical solutions of nonlinear fourth-order differential equation with a finite difference method. A non-recurrence…
In this paper, we introduce the notion of weak core and central weak core inverse in a {\it proper $*$-ring}. We further elaborate on these two classes by producing a few representations and characterizations of the weak core and central…
We study extensions of the GD tensor inverse using the M-product. The aim of current research is threefold. In the first place, the tensor GD inverse under the M-product is introduced and considered. We give the several properties and…
We address the general mathematical problem of computing the inverse $p$-th root of a given matrix in an efficient way. A new method to construct iteration functions that allow calculating arbitrary $p$-th roots and their inverses of…
In this paper, we provide a few properties of the weighted Moore--Penrose inverse for an arbitrary order tensor via the Einstein product. We again obtain some new sufficient conditions for the reverse-order law of the weighted…
Let $W_n$ denote the wheel graph having $n$-vertices. If $i$ and $j$ are any two vertices of $W_n$, define \[d_{ij}:= \begin{cases} 0 & \mbox{if}~i=j \\ 1 & \mbox{if}~i~ \mbox{and} ~j~ \mbox{are adjacent} \\ 2 & \mbox{else}. \end{cases}\]…