Sentence examples for maximal rank of from inspiring English sources
Therefore, the maximal rank of the signal matrix is definitely no more than the number of views.
It follows that the number of incident sources should be less than the maximal rank of the data covariance matrix.
A condition of a maximal rank of the force density matrix and minimal member length, were included in the form-finding procedure to guide the search of a state of self-stress with minimal elastic potential energy.
For example, a matrix equation AXB = C is consistent if and only if the minimal rank of C-AXB with respect to X is zero, see [4 6]; there is matrix X such that the partial matrix AXB of order n is nonsingular if and only if the maximal rank of AXB with respect to X is n, see [7 11].
When the "uni-vector-sensor" algorithm [2] is used in the present array-geometry, the maximal rank of the data covariance matrix equals 7. On the other hand, For the collocated electromagnetic vector-sensor [2], non-collocating electromagnetic vector-sensor [45], or the "Displaced Dipole-Triad-Plus-Loop-Triad Pair" [44], it equals 6.
Substituting (8 - 11) into (7) and (6) yield (5). Recall a simple fact that a matrix equation AXB = C is consistent for every variant matrices X, if and only if the maximal rank of C - AXB with respect to X is zero.
end{aligned}By the equivariance of (exp,), we also know that it is everywhere of maximal rank on (mathcal {C},).
The maximal rank property of (exp ) then implies that (M = mathrm {im}(exp : mathcal {C} rightarrow mathrm {Fix} (psi )^0)) is open in (mathrm {Fix} (psi )^0).
Suppose Δ ν x, u n = 0, ν = 1, 2,..., l. is a system of differential equations of maximal rank defined over M ⊂ X × U.
64 (1976) 97; Optimization and Nonsmooth Analysis, Wiley, New York, 1983) says that if πx∂H ȳ,x̄) is of maximal rank, then there exist a neighborhood Y of ȳ and a Lipschitz function G Y→Rn such that G ȳ)=x̄ and for every y in Y, H y,G y))=0.
Hence (l=1) and by assumption it follows that (phi (Omega ) subset Omega.) Let h be a limit function of ({phi ^n}) of maximal rank (say (r_phi)), i.e., begin{aligned} h(p)=lim _{j rightarrow infty } phi ^{n_j}(p) ;; text {for every};; p in Omega, end{aligned}where ({n_j}) is an increasing subsequence of natural numbers.
