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.
References in periodicals archive ?
Then the dynamic model of the spindle is established and the characteristic polynomial is obtained.
0] is a pair of conjugate purely imaginary characteristic roots and substituting [lambda] = i[omega] into the characteristic polynomial as well as letting f([omega]) = 0, we obtain
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.
The characteristic polynomial of G is a polynomial of degree n , defined as (G, ) = det (In Eqs.
m](1/t) is the characteristic polynomial which determines the recurrence relation that [h.
1)--in particular the characteristic polynomial [gamma]N of A itself--in less than 6N additions (subtractions) and less than 4N multiplications (divisions), it is entirely feasible to find the roots of this polynomial (the eigenvalues of A) by Sturm plus bisection.
Then [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the characteristic polynomial which determines the recurrence relation that [h.
Thus, the closed loop characteristic polynomial is (for simplicity, the operator [q.
S]([lambda]) is the characteristic polynomial of the shape operator of M, then we have
The Factorization Theorem [9] states that, for any free arrangement A, the characteristic polynomial of A factors completely over the integers.
2] (say) and the characteristic polynomial can be written as
i](f) are reflection vectors of the characteristic polynomial f(z) of the nominal closed-loop system (3).

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