# imaginary axis

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Related to imaginary axis: complex number

## imaginary axis

[ə′maj·ə‚ner·ē ′ak·səs]
(mathematics)
All complex numbers x + iy where x = 0; the vertical coordinate axis for the complex plane.
References in periodicals archive ?
Therefore dividing an imaginary number by i takes that imaginary number from the imaginary axis and onto the real axis in exactly the opposite way that multiplying a real number by i takes that real number from the real axis onto the imaginary axis.
GAMMA] is the subgroup of orientation-preserving isometries of a Fuchsian reflection group containing the reflection in the imaginary axis.
The tops of the curves are on the valid axis which is perpendicular to the imaginary axis, while their curvature decreases with the growth of molecular mass.
Obviously, the Hamiltonian Krylov-Schur-type method locates all eigenvalues on the imaginary axis as expected from theory while for the eigenvalues computed by eigs, it is rather difficult to decide whether or not these are purely imaginary even though the real parts are relatively small.
For a discussion of the problem of eigenvalues close to the imaginary axis (including "small" eigenvalues) see Section 3.
Therefore, in this paper, we will develop an implementation of the SR algorithm which can deal with eigenvalues on the imaginary axis.
Let Y [subset] S be the class of these functions in S which have real coefficient and which are convex in the direction of the imaginary axis.
Lemma 5: There it exists an intersection of the Mikhaylov plot with the imaginary axis for some [omega] > 0 iff a [greater than or equal to] 0 and
So as not to create any misunderstanding at this point: it is not that several vector groups (one vector pair, VP, and one EV each) are placed in a hyperbolic orthogonal space with two real axes and one imaginary axis but each vector group has its own hyperbolic space.
Proposition 3: There always exists an intersection of the Mikhaylov curve with the imaginary axis.
The imaginary axis then represents a stability border.

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