characteristic polynomial


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characteristic polynomial

[‚kar·ik·tə′ris·tik ‚päl·ə′nō·mē·əl]
(mathematics)
The polynomial whose roots are the eigenvalues of a given linear transformation on a finite dimensional vector space.
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BAUER, On certain methods for expanding the characteristic polynomial, Numer.
THE LANCZOS ALGORITHM AND COMPLEX GAUSS QUADRATURE
To study the damping properties of EMS on the basis of the structural circuit, the transfer functions are obtained for the control and disturbing actions, of which, as in the source [10], the characteristic polynomial (CP) is used:
SYNTHESIS OF A TWO-MASS ELECTRIC DRIVE WITH AN ASTATIC SYSTEM OF SUBORDINATE REGULATION AT THE ACTION OF VARIABLE FRICTION FORCES
We give a conjecture about the growth rate of M([[??].sup.[infinity].sub.n]), and the growth rates (maximal roots of the characteristic polynomial [D.sub.n]([lambda])) are computed using the softwares Drive6 and Mathematica.
Some Recurrence Relations and Hilbert Series of Right-Angled Affine Artin Monoid M([[??].sup.[infinity].sub.n])
Then the dynamic model of the spindle is established and the characteristic polynomial is obtained.
An efficient method for calculating damped critical speeds of a build-in motorized spindle
According to the Schur-Cohn stability criterion [12], when all the eigenvalues of the characteristic polynomial corresponding to the Jacobian matrix (10) are in the unit circle on the complex plane, that is, the modulus of any eigenvalue is less than 1, the equilibrium point ([x.sub.1], [x.sub.2], [I.sub.1], [I.sub.2]) is asymptotically stable.
Nonlinear Complex Dynamics of Carbon Emission Reduction Cournot Game with Bounded Rationality
Let [psi](A(G);x) = det(x[I.sub.n] - A(g)), or simply [psi](A(G)) ([psi](L(G)) and [psi](Q(G)), resp.), be the adjacency (Laplacian and signless Laplacian, resp.) characteristic polynomial of G and its roots be the adjacency (Laplacian and signless Laplacian, resp.) eigenvalues of G, denoted by [[lambda].sub.1] (G) [greater than or equal to] [[lambda].sub.2](G) [greater than or equal to] ...
Generalized Characteristic Polynomials of Join Graphs and Their Applications
A final section describes physical visualizations of eigenvectors--for mirror reflections, rotations, row reductions, and circulant matrices--before turning to the issue of their calculation through the characteristic polynomial. ([umlaut] Ringgold, Inc., Portland, OR)
Fundamentals of Matrix Analysis With Applications
The characteristic polynomial of G is a polynomial of degree n , defined as (G, ) = det (In Eqs.
INERTIA, NULLITY AND SIGNATURE OF CNC4 [n] NANOCONEi
Then [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the characteristic polynomial which determines the recurrence relation that [h.sub.m](n) satisfies.
A conjecture on the number of hamiltonian cycles on thin grid cylinder graphs
Then [[chi].sub.m](t) = [t.sup.dm] [q.sub.m](1/t) is the characteristic polynomial which determines the recurrence relation that [h.sub.m](n) satisfies.
A conjecture on the number of Hamiltonian cycles on thin grid cylinder graphs
Thus, the closed loop characteristic polynomial is (for simplicity, the operator [q.sup.-1] is omitted)
Self tuning regulators for a liquid level process

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