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 generali
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. ...
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The analysis is developed from the theory of linear constant coefficient systems via linear variable coefficient systems to general nonlinear systems. Further sections on control problems, generalized inverses of differential-algebraic operators, generalized solutions, and differential equations on manifolds ...
The algebraic nature of generalized inverses is presented, and the behavior of generalized inverses are related to the properties of the algebraic system. Scholars and graduate students working on the theory of rings, semigroups and generalized inverses of matrices and operators will find this book ...
The analysis is developed from the theory of linear constant coefficient systems via linear variable coefficient systems to general nonlinear systems. Further sections on control problems, generalized inverses of differential-algebraic operators, generalized solutions, and differential equations on manifolds ...
Mathematics - Category Theory55U3518G3018E35We modify a previous result, which showed that certain diagrams of spaces are essentially simplicial monoids, to construct diagrams of spaces which model simplicial groups. Furthermore, we show that these diagrams can be generalized to models for Segal ...
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 ...
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 ...