Book abstract: This book presents the theory of time-variant systems, or equivalently, recursive matrix operations, based on a novel unifying and elementary computational approach. It consists of a set of 11 lectures on basics, followed by several deeper applications of systems theory to matrix algebra, illustrating the power of the basic theory. As a result, it offers an accessible, complete and theoretically fully motivated unifying workbench for electrical engineers, numerical analysts and signal-processing engineers, who need to understand how systems behave, how computational efficiency can be enhanced algorithmically and how recursive algorithms can be mastered. To achieve this, the approach is fully vested in the basic principles of modern systems theory as they present themselves in time-variant environments. As a further illustration of the power of the basic theory, the book presents original solutions to several major issues in matrix algebra, to wit efficient Moore–Penrose inversion, LU and spectral factorizations, constrained approximation and interpolation, scattering theory and embedding theory.
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