Sentence examples for matrix pencil lambda from inspiring English sources

Let (m_{s}) and (m_{u}) denote the number of singularities of matrix pencil (lambda E -G), which lie inside and outside the open unit disk, respectively.

Note that the singularities of the matrix pencil (lambda E-G), i.e. the roots of (det(lambda E-G =0) E-G =0arely thexactly of the equation (det(D(lambda ))=0), wherootsD(lambda )= D_{0}+D_{1}lambda +ldofs +D_{L+1}{lambda }^{L+1}).

There are a number of applications for generalized singular-value decomposition (GSVD) in the literature including the computation of the Kronecker form of the matrix pencil (A - lambda B) [5], solving linear matrix equations [1], weighted least squares [2], and linear discriminant analysis [6] to name but a few.

Under the zero initial condition, the frequency domain description for system (4) is begin{aligned} &bigl sE(p -A(p -Agr)x(s,p bigr)u(s), &y(s,p)=C(p)x s,p =D(p)u(s), end{aligned} (10) where we assume that the matrix pencil ((A(p),E(p))) is regular for any p value, i.e., there exists (lamBda_{p u s such that (lambda _{p,0}E(p)-A(p)) is nonsingular.

(ii) Matrix pencil ( E, A ) with no finite eigenvalue  .

Matrix pencil ( E, A ) with no finite eigenvalues.

Matrix pencil ( E, A ) with at least one finite eigenvalue.

A matrix pencil is a family of matrices sF - G, parametrized by a complex number s.

Figure 6 Sparsity of matrix pencil ( E, A ). Figure 7 Sparsity of matrix pencil ( E ˜, A ˜ ). Figure 8 Output solutions of Example 5.

(i) Matrix pencil ( E, A ) with at least one finite eigenvalue  .

Moreover, this decoupling preserves the spectrum of the matrix pencil ( E, A ) of the DAE.