The generalized inverse is an algebraic notion and it is of some interest to ask what the structure of a Hilbert space has to do with it. Positivity can be imposed on the theory ex post facto after the generalized inverse has been defined over an arbitrary field. The chapter develops the ...
Nashed, M.Z., Votruba, G.F.: A unified operator theory of generalized inverses. In: Generalized Inverses and Applications (Proc. Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1973), pp. 1–109. Publication of Mathematics Research Center University Wisconsin, No. 32. Academic...
Öystein O.: Contributions to the theory of finite fields. Trans. Am. Math. Soc. 36(2), 243–274 (1934). Article MathSciNet Google Scholar Pascal B.: Traité du triangle arithmétique, Chez Guillaume Desprez (1965). Rijmen V., Barreto P.S., Gazzoni Filho D.L.: Rotation symmetry...
representation of a quaternion matrix, we introduce a concept of norm of quaternion matrices, discuss singular values and generalized inverses of a quaternion matrix, study the QLS problem and derive two algebraic methods for finding solutions of the QLS problem in quaternionic quantum theory. ...
This is the first comprehensive textbook that provides a systematic and detailed analysis of initial and boundary value problems for differential-algebraic equations. The analysis is developed from the theory of linear constant coefficient systems via linear variable coefficient systems to general nonlinear...
The idea here, for both monoids and groups, is that when we consider diagrams of spaces given by a particular algebraic theory, from a homotopy-theoretic perspective we can actually consider diagram...Julia E. Bergner. Adding inverses to diagrams encoding algebraic structures. Homology, Ho- ...
Some concepts in semigroup theory can be interpreted in several algebraic structures. A generalization fA,B,fA,B(X) = A(X′)B of the complement operator (′) on Boolean matrices is made, where A and B denote any rectangular Boolean matrices. While (′) is an isomorphism between Boolean ...
Algebraic Riccati equations (AREs) have gained considerable magnitude in applied mathematics and a range of engineering issues since Kalman showed how widely used they are in filtering and optimal control theory [1]. These problems include controlling wind generators [2], linear multi-agent systems ...
Since Kalman demonstrated the widespread use of algebraic Riccati equations (ARE) in filtering theory and optimal control [1], ARE have drawn significant attention in science, applied mathematics, and a variety of engineering problems, including controlling doubly-fed wind generators [2], wheeled inve...
The algebraic theory of surgery gives a necessary and sufficient chain level condition for a space with n-dimensional Poincare duality to be homotopy equivalent to an n-dimensional topological manifold. A relative version gives a necessary and sufficient chain level condition for a simple homotopy ...