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.
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. ...
The following theorem is a generalization of the solution theory of the abstract Cauchy problem \(\frac{d}{dt} x(t)=Ax(t)\), \(x(0)=x_0\) and extends the proofs of [10, p. 34] and [16, Ch. 4, Thm. 1.2] to the DAE case with the help of pseudo-resolvents.Theorem 2.2Ass...
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 ...
Asχnis used in so many cryptographic applications, it is important to understand these maps very well. Each of the properties ofχncould be exploited in an attack, or conversely be used to argue for security properties. For instance, in [8] and [9], the differential and correlation proper...
This method is by far known as the most efficient method for solving large-scale algebraic system of equations [20], [21], [22]. Their convergence rate is often independent of the mesh size, and such optimal convergence theory can be found, for instance, in [20], [4], [43]. On ...
It is not hard to see, with the above initial A0,G0 and H0, that the SDA_ls still works, again with exactly the same forms and updating formulae for Ak,Bk,Ck,Dk(1),Dk(2) and the inverses of Rk,Sk and Tk. One relevant difference for CAREs is that A0≠A but satisfies, from ...
This paper is a review of the algebraic theory of convolutional codes through the focus of the author’s 1970 paper [F1], including its origins in the work of Kalman et al. and of Massey and Sain. This paper grew out of and in turn influenced the develop
(1974): On the discrete linear L1 approximation and L1 solutions of overdetermined linear equations, J. Approximation Theory 11 (1974), 38-53 Google Scholar Adler, R. and Pelzer, H. (1994): Development of a Long Term Geodetic Monitoring System of Recent Crustal Activity Along the Dead Sea...
This finding contributes to the larger theory of perceptual learning (Goldstone et al., 2017, Kellman et al., 2010), which suggests that thinking, learning, and problem solving are grounded in the environment and that the ways in which problems are presented influence how individuals process ...