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Algebra --- Matrices --- Matrices. --- Linear operators --- Opérateurs linéaires --- Generalized inverses --- Inverses généralisés --- Inverses généralisés. --- Opérateurs linéaires --- Generalized inverses. --- Inverses généralisés --- Algebre lineaire --- Methodes variationnelles --- Determinants

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Most of the existing monographs on generalized inverses are based on linear algebra tools and geometric methods of Banach (Hilbert) spaces to introduce generalized inverses of complex matrices and operators and their related applications, or focus on generalized inverses of matrices over special rings like division rings and integral domains, and does not include the results in general algebraic structures such as arbitrary rings, semigroups and categories, which are precisely the most general cases. In this book, five important generalized inverses are introduced in these algebraic structures. Moreover, noting that the (pseudo) core inverse was introduced in the last decade and has attracted much attention, this book also covers the very rich research results on it, so as to be a necessary supplement to the existing monographs. This book starts with decompositions of matrices, introduces the basic properties of generalized inverses of matrices, and then discusses generalized inverses of elements in rings and semigroups, as well as morphisms in categories. 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 helpful.

Linear operators --- Generalized inverses. --- Operadors lineals --- Associative rings. --- Associative algebras. --- Group theory. --- Associative Rings and Algebras. --- Group Theory and Generalizations.

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Matrices --- Linear operators --- Opérateurs linéaires --- Generalized inverses --- Inverses généralisés --- Opérateurs linéaires --- Inverses généralisés

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Operator theory --- 517.983 --- 519.6 --- 681.3*G13 --- Linear operators. Linear operator equations --- Computational mathematics. Numerical analysis. Computer programming --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- Approximation theory. --- Hilbert space. --- Linear operators --- Generalized inverses. --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 517.983 Linear operators. Linear operator equations --- Approximation theory --- Hilbert space --- Generalized inverses of linear operators --- Inverses of linear operators, Generalized --- Matrix inversion --- Banach spaces --- Hyperspace --- Inner product spaces --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Generalized inverses

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Numerical approximation theory --- Matrix inversion --- Transformations (Mathematics) --- Matrices --- Transformations (Mathématiques) --- Inversion --- 512.64 --- Algorithms --- Differential invariants --- Geometry, Differential --- Inverse matrices --- Inverse of a matrix --- Inversion, Matrix --- Linear operators --- Linear and multilinear algebra. Matrix theory --- Generalized inverses --- Matrix inversion. --- Transformations (Mathematics). --- 512.64 Linear and multilinear algebra. Matrix theory --- MATRIX INVERSION --- Opérateurs linéaires --- Inverses généralisés --- Opérateurs linéaires --- Inverses généralisés