By examining the real part of the

complex conjugate paired eigen values, the stability of the torsional vibration modes they represent can be determined.

There is one real root apparent at x = 1 but no indication whatsoever of the whereabouts of the

complex conjugate roots.

Then the eigenvalues of A are real or occur in

complex conjugate pairs.

The conversion gain achieved after creating a pair of

complex conjugate poles, with negative real part [r.

k] at k[pi]/[sigma], k [not equal to] 0, a value [epsilon] at z = 0, having simple zeros in (-[pi]/[sigma], 0) and (0, [pi]/[sigma]), and m - 1

complex conjugate zeros close to z = 0.

Because the inner products cancel when

complex conjugates are multiplied

50), then d, and y (they are the

complex conjugates of d, y) are solutions to Eqs.

Since the TF denominator of the stable circuit is the Hurwitz polynomial, the roots of this polynomial can be either real negative, or they can form the

complex conjugate pairs with negative real part.

B(s) equal to zero (note that minus sign correspond to the

complex conjugate pole of transfer function)--with [[sigma].

n,m], A* denotes the

complex conjugate and transpose of A [member of] [C.

1) [Mathematical Expression Omitted] (2) [Mathematical Expression Omitted] where <> = the time average * = the

complex conjugate N is a Hermitian matrix, that is, its nondiagonal elements are

complex conjugates of each other, which will be true of all power correlation matrices.

The non-real n-th roots of unity always form

complex conjugate pairs.