This is the first comprehensive textbook that provides a systematic and detailed analysis of initial and boundary value problems for differential-algebraic equations. The analysis is developed from the theory of linear constant coefficient systems via linear variable coefficient systems to general nonlinear...
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. ...
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 ...
Nashed, M.Z., Votruba, G.F.: A unified operator theory of generalized inverses. In: Generalized Inverses and Applications (Proc. Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1973), pp. 1–109. Publication of Mathematics Research Center University Wisconsin, No. 32. Academic...
(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...
Since [Math Processing Error]SN(−1) and [Math Processing Error]S(−1)N are inverses of one another, it is sufficient to compute the inverse of both sides of the result from Lemma 2. Note that the only change on the right side will be that S inverts to N. [Math Processing Erro...
Guillemin (1996): Measure theory and probability, 2nd edition, Birkhäuser-Verlag, Basel Boston Berlin 1996 Google Scholar Adelmalek, N.N. (1974): On the discrete linear L1 approximation and L1 solutions of overdetermined linear equations, J. Approximation Theory 11 (1974), 38-53 Google ...
, X k are a family of matrices with variable entries. The purpose of this paper is to propose and investigate the relationships between certain linear matrix functions that regularly appear in matrix theory and its applications. We shall derive a series of meaningful, necessary, and sufficient co...
Since Kalman demonstrated the widespread use of algebraic Riccati equations (ARE) in filtering theory and optimal control [1], ARE have drawn significant attention in science, applied mathematics, and a variety of engineering problems, including controlling doubly-fed wind generators [2], wheeled inve...
Standard Genetic Code Group theory is the branch of mathematics that is used for studying symmetry. In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. 2.1. The Concept of a Group ...