Generalized Inverses: Theory and Computations

This book begins with the fundamentals of the generalized inverses, then moves to more advanced topics.

It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the generalized inverses, perturbation analysis of the generalized inverses, an algorithmic study of the computational methods for the full-rank factorization of a generalized inverse, generalized singular value decomposition, imbedding method, finite method, generalized inverses of polynomial matrices, and generalized inverses of linear operators. This book is intended for researchers, postdocs, and graduate students in the area of the generalized inverses with an undergraduate-level understanding of linear algebra.

Aceasta carte incepe cu fundamentele inverselor generalizate, apoi trece la subiecte mai avansate. Prezinta un studiu teoretic al generalizarii regulii lui Cramer, reprezentari determinante ale inverselor generalizate, legea ordinii inverse a inverselor generalizate ale unui produs matricial, structuri a inverselor generalizate ale matricelor structurate, calcul paralel al inverselor generalizate, analiza perturbatiei inverselor generalizate, un studiu algoritmic al metodelor de calcul pentru factorizarea completa a unui invers generalizat, descompunerea valorii singularizate generalizate, metoda de incorporare, metoda finita , inversele generalizate ale matricilor polinomiale si inversele generalizate ale operatorilor liniari.