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In the modal reduction, the dynamic condensation matrix is directly computed from the eigenvector matrix of full model.
Let (A inmathbb{R}^{m times n}) be an underdetermined matrix of full rank, and denote (Omega^=|operatorname{support} (A^{T} AA^{T})^{-1}b)|).
where C and Q are closed convex sets of R n, and A is an n × n matrix of full rank.
end{aligned} (36 For complete markets given (mathbf {n}_i^) there is a unique solution for (mathbf {n}_i) since (mathbf {X}) is a square matrix of full rank.
This is because, H n is a Rayleigh-fading channel matrix of full rank (with probability 1) due to (A1) and (C1) stipulates that Q be a full column-rank matrix.
end{aligned} Since (G(x^{(0)} -Upsilon(G(x^{(0)} -Upsilonand (nabla h(x)^{T}) is a matrix of full row rank, by the parameterized Sard theorem and the inverse imaGe theorem, (H_{P^{(0)}}^{-1}(0)) consists of some smooth curves.
Similar(49)
Rayleigh fading matrix channel, the channel matrix is of full rank with probability one [16, 17].
Controllability can be tested by the rank of controllability matrix; if the controllability matrix is of full rank, then the system is controllable, otherwise uncontrollable.
where is the complex exponential coefficients modeling the LTV channel, and is a matrix with Thus, when the matrix is of full column rank, and the basis exponential model coefficients can be estimated by. (16).
Hence, D ≠ 0, so the matrix is of full rank.
Generically, the mixing matrix is of full rank and of full k-rank when the parameters it involves are drawn from continuous probability densities.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com