Sentence examples for multiple eigenvalues and from inspiring English sources

The results can be used to define the sensitivity of the semisimple multiple eigenvalues and corresponding generalized eigenvector matrices.

This paper considers the sensitivity of semisimple multiple eigenvalues and corresponding generalized eigenvector matrices of a nonsymmetric matrix pencil analytically dependent on several parameters.

We finally present a procedure for constructing a tridiagonal matrix with specified multiple eigenvalues, and then give four examples for the resulting procedure.

In the non-selfadjoint case, there may be a finite number of multiple eigenvalues and, hence, for unique determination of the Sturm-Liouville operator, one should specify some additional information.

So, the tridiagonal matrix T is not a diagonalizable matrix with the same complex multiple eigenvalues and real distinct ones as A. In this paper, we clarify that the qd recursion formula is applicable to constructing a tridiagonal matrix with specified multiple eigenvalues.

We also discuss the characteristic and the minimal polynomials of a tridiagonal matrix in Section 4. In Section 5, we design a procedure for constructing a tridiagonal matrix with specified multiple eigenvalues, and then demonstrate four tridiagonal matrices as examples of the resulting procedure.

If A has a zero multiple eigenvalue and b=c=0, then in addition to the two solutions in (4), an infinite number of solutions exist as the following for (2): X = a c a − a, X = − a c a a, X = β γ α − β 2 γ − β, Open image in new window.

The directional derivatives of the multiple eigenvalues are obtained, and the average of eigenvalues and corresponding generalized eigenvector matrices are proved to be analytic.

Note that there can be multiple eigenvalues, their multiplicities are finite and equal to (m - operatorname{rank} u(rho_{k})).

Consequently, solutions of (2) are bounded for k ∈ Z if and only if all eigenvalues of U N have modulus one and are of simple type, i.e., multiple eigenvalues have the same algebraic and geometric multiplicity.

By (4.15) is a multiple eigenvalue if and only if (456).