About the book
An inverse problem, which starts with the causes and then calculates the effects, covers many fields of science. In many cases, models of given inverse problems can be linearized which allows the use of methods of linear algebra for their solutions. Effective tools of linear algebra in linear inverse problems are, in particular, generalized inverse matrices as one of the ways to represent (pseudo)solutions to singular (differential) matrix equations. Nowadays, the theory of generalized inverses is one of the hot topics of linear algebra in various aspects, such as elements of the ring, operators of Hilbert space, or matrices with real, complex, and quaternion entries. Matrices over quaternion algebra are also useful tools in a lot of applied inverse problems, among them in signal and color image processing, quantum physics, etc. In recent years, methods of simultaneous decompositions for tensors have been actively used in different inverse problems. In particular, a product singular value decomposition of a quaternion tensor triplet (higher-order PSVD) has various applications in digital watermarking technology. The main goals of this book are both to give the last achievements in various areas of linear algebra, such as generalized inverses and their applications in solving matrix equations and matrix minimization problems, decompositions of matrices and tensors, new developments in theories of quaternion matrices, and operators of Hilbert space, etc. It is also important to consider new applying models of inverse problems that can be linearized.
