flimsy
发表于 2025-3-28 18:35:25
State Space Linear Systems: Formal Definitions and General Propertiesch systems exhibit. The treatment may be viewed as an effort to make precise some of the notions described heuristically in the Introduction. Specifically, . should serve as . for “real-world” processes which take input “time functions” to output “time functions” in some linear fashion. The real-wor
同位素
发表于 2025-3-28 19:56:55
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Bouquet
发表于 2025-3-29 02:07:42
Eigenvectors, Eigenvalues, and Normal Modesnsion n may be .; that is to say, there exist for most such systems real constant matrices ., ., ., and . having respective sizes (. × .), (. × .), (. × .), and (. × .) such that the system’s behavior may be analyzed in terms of the equations.
hallow
发表于 2025-3-29 05:24:43
The , + , Decomposition for Matrices Which Are Not Semi-Simplets about the linear mappings ..: R. → R. and .-C. → C., but also to procedures which may, at least in principle, be used in computing . and .. In the pages which follow, we focus attention on matrices A which are not semi-simple (hence, in particular, not diagonalizable); the techniques we shall be
AVID
发表于 2025-3-29 11:09:22
Complex Matrices and the Unitary Diagonalizabity of Hermitian Matricesapplied only to real (. × .) matrices A, the truth is that just about everything said in §§8–9 about real matrices has its analogue in the theory of . matrices. Let us go through §§8–9 point by point and isolate the (few) instances where realness of . makes a difference.
预感
发表于 2025-3-29 15:25:55
Nilpotent Matrices and the Jordan Canonical Formtrix of the linear transformation. C. with respect to a special basis for C.. We saw in §9 that if the distinct eigenvalues of . are . (λ.),…, λ., with respective generalized eigenspaces .(λ.),…, .(λ.), and if z.is a basis for .(λ.), 1 ⩽ . ⩽ . then the matrix of . with respect to the ordered basis z
Rotator-Cuff
发表于 2025-3-29 17:25:15
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刻苦读书
发表于 2025-3-29 23:22:28
Reachability and Controllability for Time-Invariant Continuous-Time Systems In §6, we presented a formal definition of .; such a system is a composite mathematical object with various components: the space U of . -vector input functions, the spaces . of . -vector output functions, the (finite-dimensional) state space ., the state transition mapping ., and the readout mappi
dagger
发表于 2025-3-30 01:17:56
Reachability and Controllability for Time-Invariant Discrete-Time Systemsit easier than the proofs of their continuous-time analogues; much of the technical machinery which we shall require is already at hand. As in §13, various definitions and results are stated and proved both in the context of “abstract” discrete-time linear systems, as per Definition 6.2, and in the
AGATE
发表于 2025-3-30 05:38:00
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