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Given any matrices A,B,C,D such that the products below are defined, then the invertibility of A, D, and D - C[A.
Based on the definition of invertibility, the result demonstrates clearly the non-invertibility of the V-matrix based watermarking since the attacker was unable to extract his faked watermark [W.
In this case the invertibility conditions (ii) in Theorems 4.
35) There is no general proof of invertibility of [I - A[OMEGA], but if A[OMEGA] were by chance to have some eigenvalue exactly equal to 1.
2001), the minimum singular value is a measure of the invertibility of the system and, therefore, represents a measure of potential problems of the system under the action of feedback controllers.
Charecterization of W- maps in terms of invertibility, Bulletin of Pure and Applied Sciences, Vol.
It should be acknowledged that the invertibility of A is not necessary: in the case of a singular A, which implies a vanishing symbol f, we have g(x) = [f.
The non invertibility of the conditional model into marginal model can be used as evidence of super-exogeneity because the invertibility of conditional model into marginal model is precluded if the variables are super exogenous for the parameters of the conditional model [Hendry and Ericsson (1991)].
Implications for stationarity, invertibility, memory, and stability are also discussed.
Localization of Frames, Banach Frames, and the Invertibility of the Frame Operator.
In this case the result requires the invertibility of the matrix I - [mu](t) [f.
Assuming robust stability and invertibility of the operator (I + NQ - LQ), explicit bounds on the control-relevant non-linearity are obtained.