Sentence examples for as its eigenvalues from inspiring English sources
Given a pattern Λ, the approximation in (13) requires finding the Markov chain imbedding associated with the waiting time W, the essential transition probability matrix N as well as its eigenvalues and associated eigenvectors.
It is shown that given a set of n not necessarily distinct nonreal numbers in the open upper (lower) half-plane uniquely determines an n×n Jacobi matrix with a rank-one imaginary part having those numbers as its eigenvalues counting algebraic multiplicity.
We considered the case that A only has 0 or l i 2 ω 2 as its eigenvalues, where ω = 2 π / T, l i ∈ N, i = 1, …, r and 0 ≤ r ≤ N. In [17], we used the following condition which presents some advantages over (1.3) and (1.4): (H) there exist positive constants m, ζ, η and ν ∈ [ 0, 2 ) such that ( 2 + 1 ζ + η | x | ν ) F ( t, x ) ≤ ( ∇ F ( t, x ), x ), x ∈ R N, | x | > m a.e. t ∈ [ 0, T ]. .
In particular, the result is valid for the polyharmonic Newton potential operator, which is related to a nonlocal boundary value problem for the poly-Laplacian extending the one considered by M. Kac in the case of the Laplacian, so we obtain isoperimetric inequalities for its eigenvalues as well, namely, analogues of Rayleigh Faber Krahn and Hong Krahn Szegö inequalities.
A natural way to construct diffusion tensor D is from structure tensor J such that D has the same eigenvectors as J and its eigenvalues prefer the diffusion along the coherent direction than across to it.
As such, all of its eigenvalues are zero.
Consider its eigenvalues as follows: λ 1 = a + d 2, λ 2 = a + d 2 + t, ( t → 0 ).
Its eigenvalues as an equilibrium of the corresponding desingularized reduced system are −μ and −1; thus, the folded singularity is a node for (mu >0).
We explicitly calculate the FIM for this model with (n=10) at low temperature, and Figure 3(a) shows its eigenvalues as a function of (B^{0}).
Then, left[ begin{array}{cc} text{diag} y) y^{top} end{array}right] left[begin{array}{ll} text{diag} y) & y end{array}right] =left[ begin{array}{ll} I_{m} & {1}_{m} {1}_{m}^{top} & m end{array} right], which is a special arrow-head matrix and has m+1 as its largest eigenvalue (see [29]).
